Finite Group Databasebeta

← Group #10844792

Character table — Group #10844792

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12222222344444444666666612121212121212124488888888121212121212121224242424242424242424242424242424224444446666121212121212121212121212444488882244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ911111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ1011111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ1111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-111-1-1-11-11
χ1211111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-1111-11-1
χ1311111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1-1-111-111-1
χ1411111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1111-1-11-1-11
χ1511111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-111111-11-1-1-1111-1-11
χ1611111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-11-1111-1-1-111-1
χ17222222222-2-22222-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-200000000
χ18222222222-2-22222-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-22222-2-200000000000000000000000000000000000000002-2-2200000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-22222-2-20000000000000000000000000000000000000000-222-200000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000
χ292222-2-2-2-222-20000-222-22-22-2-200000000002i2i−2i−2i00002-200002-22i2i2i2i−2i−2i−2i−2i000000002-22i−2i000022-2-22i2i−2i−2i00000000000000000000
χ302222-2-2-2-222-20000-222-22-22-2-200000000002i2i−2i−2i00002-200002-22i2i2i2i−2i−2i−2i−2i00000000-22−2i2i0000-2-222−2i−2i2i2i00000000000000000000
χ312222-2-2-2-222-20000-222-22-22-2-20000000000−2i−2i2i2i00002-200002-2−2i−2i−2i−2i2i2i2i2i000000002-2−2i2i000022-2-2−2i−2i2i2i00000000000000000000
χ322222-2-2-2-222-20000-222-22-22-2-20000000000−2i−2i2i2i00002-200002-2−2i−2i−2i−2i2i2i2i2i00000000-222i−2i0000-2-2222i2i−2i−2i00000000000000000000
χ332222-2-2-2-2-12-20000-22-11-11-1113333−3−3−3−3002i2i−2i−2i0000-1133−3−3-11−i−i−i−iiiii−i3−i3−i3−i3i3i3i3i32-22i−2i0000-1-111−i−iii−i3−i3i3i333−3−3000000000000
χ342222-2-2-2-2-12-20000-22-11-11-1113333−3−3−3−3002i2i−2i−2i0000-1133−3−3-11−i−i−i−iiiii−i3−i3−i3−i3i3i3i3i3-22−2i2i000011-1-1ii−i−ii3i3−i3−i3−3−333000000000000
χ352222-2-2-2-2-12-20000-22-11-11-1113333−3−3−3−300−2i−2i2i2i0000-1133−3−3-11iiii−i−i−i−ii3i3i3i3−i3−i3−i3−i32-2−2i2i0000-1-111ii−i−ii3i3−i3−i333−3−3000000000000
χ362222-2-2-2-2-12-20000-22-11-11-1113333−3−3−3−300−2i−2i2i2i0000-1133−3−3-11iiii−i−i−i−ii3i3i3i3−i3−i3−i3−i3-222i−2i000011-1-1−i−iii−i3−i3i3i3−3−333000000000000
χ372222-2-2-2-2-12-20000-22-11-11-111−3−3−3−33333002i2i−2i−2i0000-11−3−333-11−i−i−i−iiiiii3i3i3i3−i3−i3−i3−i32-22i−2i0000-1-111−i−iiii3i3−i3−i3−3−333000000000000
χ382222-2-2-2-2-12-20000-22-11-11-111−3−3−3−33333002i2i−2i−2i0000-11−3−333-11−i−i−i−iiiiii3i3i3i3−i3−i3−i3−i3-22−2i2i000011-1-1ii−i−i−i3−i3i3i333−3−3000000000000
χ392222-2-2-2-2-12-20000-22-11-11-111−3−3−3−3333300−2i−2i2i2i0000-11−3−333-11iiii−i−i−i−i−i3−i3−i3−i3i3i3i3i32-2−2i2i0000-1-111ii−i−i−i3−i3i3i3−3−333000000000000
χ402222-2-2-2-2-12-20000-22-11-11-111−3−3−3−3333300−2i−2i2i2i0000-11−3−333-11iiii−i−i−i−i−i3−i3−i3−i3i3i3i3i3-222i−2i000011-1-1−i−iiii3i3−i3−i333−3−3000000000000
χ412-22-22-2-2222-200002-2-222-2-22-200000000002-22-200002-20000-2222-2-222-2-20000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000
χ422-22-22-2-2222-200002-2-222-2-22-200000000002-22-200002-20000-2222-2-222-2-2000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000
χ432-22-22-2-2222-200002-2-222-2-22-20000000000-22-2200002-20000-22-2-222-2-2220000000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i000000000000
χ442-22-22-2-2222-200002-2-222-2-22-20000000000-22-2200002-20000-22-2-222-2-222000000000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000000000
χ452-22-22-2-22-12-200002-21-1-111-1133−3−333−3−3002-22-20000-113−33−31-1-1-111-1-11133−3−333−3−300002i−2i2i−2i−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii000000000000
χ462-22-22-2-22-12-200002-21-1-111-1133−3−333−3−3002-22-20000-113−33−31-1-1-111-1-11133−3−333−3−30000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i000000000000
χ472-22-22-2-22-12-200002-21-1-111-1133−3−333−3−300-22-220000-113−33−31-111-1-111-1-1−3−333−3−33300002i−2i−2i2ii3−i3i3−i3−i3i3−i3i3−ii−iii−ii−i000000000000
χ482-22-22-2-22-12-200002-21-1-111-1133−3−333−3−300-22-220000-113−33−31-111-1-111-1-1−3−333−3−3330000−2i2i2i−2i−i3i3−i3i3i3−i3i3−i3i−ii−i−ii−ii000000000000
χ492-22-22-2-22-12-200002-21-1-111-11−3−333−3−333002-22-20000-11−33−331-1-1-111-1-111−3−333−3−33300002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii000000000000
χ502-22-22-2-22-12-200002-21-1-111-11−3−333−3−333002-22-20000-11−33−331-1-1-111-1-111−3−333−3−3330000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i000000000000
χ512-22-22-2-22-12-200002-21-1-111-11−3−333−3−33300-22-220000-11−33−331-111-1-111-1-133−3−333−3−300002i−2i−2i2i−i3i3−i3i3i3−i3i3−i3−ii−iii−ii−i000000000000
χ522-22-22-2-22-12-200002-21-1-111-11−3−333−3−33300-22-220000-11−33−331-111-1-111-1-133−3−333−3−30000−2i2i2i−2ii3−i3i3−i3−i3i3−i3i3i−ii−i−ii−ii000000000000
χ532-22-2-222-222222-2-2-2-2-2-222-2-2222-2-2-2-2222-22i−2i−2i2i2i2i−2i−2i222-2-22-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ542-22-2-222-222222-2-2-2-2-2-222-2-2222-2-2-2-2222-2−2i2i2i−2i−2i−2i2i2i222-2-22-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ552-22-2-222-2222-2-222-2-2-2-222-2-22-2-22222-2-2-222i−2i−2i2i−2i−2i2i2i22-222-2-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ562-22-2-222-2222-2-222-2-2-2-222-2-22-2-22222-2-2-22−2i2i2i−2i2i2i−2i−2i22-222-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ572-22-2-222-22-2-222-2-222-2-222-2-2222-2-2-2-222-2200000000-2-2-222-222000000000000000000000000000000000000000000002-22-20000
χ582-22-2-222-22-2-222-2-222-2-222-2-2222-2-2-2-222-2200000000-2-2-222-22200000000000000000000000000000000000000000000-22-220000
χ592-22-2-222-22-2-2-2-22222-2-222-2-22-2-22222-2-22-200000000-2-22-2-2222000000000000000000000000000000000000000000002-2-220000
χ602-22-2-222-22-2-2-2-22222-2-222-2-22-2-22222-2-22-200000000-2-22-2-222200000000000000000000000000000000000000000000-222-20000
χ612-22-2-222-2-12222-2-2-2-211-1-111-1-1-11111-1-12-22i−2i−2i2i2i2i−2i−2i-1-1-111-111−i−iiiii−i−iii−i−i−i−iii00000000−i3i3i3−i33−3−33−333−3−i3i3i3−i3000000000000
χ622-22-2-222-2-12222-2-2-2-211-1-111-1-1-11111-1-12-22i−2i−2i2i2i2i−2i−2i-1-1-111-111−i−iiiii−i−iii−i−i−i−iii00000000i3−i3−i3i3−333−33−3−33i3−i3−i3i3000000000000
χ632-22-2-222-2-12222-2-2-2-211-1-111-1-1-11111-1-12-2−2i2i2i−2i−2i−2i2i2i-1-1-111-111ii−i−i−i−iii−i−iiiii−i−i00000000−i3i3i3−i3−333−33−3−33−i3i3i3−i3000000000000
χ642-22-2-222-2-12222-2-2-2-211-1-111-1-1-11111-1-12-2−2i2i2i−2i−2i−2i2i2i-1-1-111-111ii−i−i−i−iii−i−iiiii−i−i00000000i3−i3−i3i33−3−33−333−3i3−i3−i3i3000000000000
χ652-22-2-222-2-122-2-222-2-211-1-111-111-1-1-1-111-222i−2i−2i2i−2i−2i2i2i-1-11-1-1111−i−iiiii−i−i−i−iiiii−i−i00000000−i3i3i3−i33−3−333−3−33i3−i3−i3i3000000000000
χ662-22-2-222-2-122-2-222-2-211-1-111-111-1-1-1-111-222i−2i−2i2i−2i−2i2i2i-1-11-1-1111−i−iiiii−i−i−i−iiiii−i−i00000000i3−i3−i3i3−333−3−333−3−i3i3i3−i3000000000000
χ672-22-2-222-2-122-2-222-2-211-1-111-111-1-1-1-111-22−2i2i2i−2i2i2i−2i−2i-1-11-1-1111ii−i−i−i−iiiii−i−i−i−iii00000000−i3i3i3−i3−333−3−333−3i3−i3−i3i3000000000000
χ682-22-2-222-2-122-2-222-2-211-1-111-111-1-1-1-111-22−2i2i2i−2i2i2i−2i−2i-1-11-1-1111ii−i−i−i−iiiii−i−i−i−iii00000000i3−i3−i3i33−3−333−3−33−i3i3i3−i3000000000000
χ6944444444-2-4-44444-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-400000000222222220000000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-222222222440000000022-2-2-2-2220000000000000000000000000000000000000000000000000000
χ714444-4-4-4-44-4400004-44-44-44-4-4000000000000000000-440000-440000000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-2-4400004-4-22-22-22223232323−23−23−23−2300000000002-2−23−2323232-20000000000000000000000000000000000000000000000000000
χ734444-4-4-4-4-2-4400004-4-22-22-222−23−23−23−232323232300000000002-22323−23−232-20000000000000000000000000000000000000000000000000000
χ7444-4-444-4-44000000004-4-44-44-400000000000000−2i22i2−2i22i20000000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ7544-4-444-4-44000000004-4-44-44-4000000000000002i2−2i22i2−2i200000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ7644-4-444-4-4-200000000-222-22-2223−2323−2323−2323−23000000−2i22i2−2i22i200000000i6−i6i6−i6i6−i6i6−i6i2−i2i2−i2i2−i2i2−i2000000000000000000000000000000000000
χ7744-4-444-4-4-200000000-222-22-2223−2323−2323−2323−230000002i2−2i22i2−2i200000000−i6i6−i6i6−i6i6−i6i6−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000000000
χ7844-4-444-4-4-200000000-222-22-22−2323−2323−2323−2323000000−2i22i2−2i22i200000000−i6i6−i6i6−i6i6−i6i6i2−i2i2−i2i2−i2i2−i2000000000000000000000000000000000000
χ7944-4-444-4-4-200000000-222-22-22−2323−2323−2323−23230000002i2−2i22i2−2i200000000i6−i6i6−i6i6−i6i6−i6−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000000000
χ8044-4-4-4-4444004-44-40044-4-4-4-444-44-4-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ8144-4-4-4-444400-44-440044-4-4-4-44-44-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ8244-4-4-4-444-2004-44-400-2-22222-2-22-222-22-20000000000000000006−66−6−66−66−66−666−66−6000000000000000000000000000000000000
χ8344-4-4-4-444-2004-44-400-2-22222-2-22-222-22-2000000000000000000−66−666−66−66−66−6−66−66000000000000000000000000000000000000
χ8444-4-4-4-444-200-44-4400-2-22222-22-22-2-22-220000000000000000006−66−6−66−666−66−6−66−66000000000000000000000000000000000000
χ8544-4-4-4-444-200-44-4400-2-22222-22-22-2-22-22000000000000000000−66−666−66−6−66−666−66−6000000000000000000000000000000000000
χ864-44-44-4-444-440000-44-444-4-44-4000000000000000000-4400004-40000000000000000000000000000000000000000000000000000
χ874-44-44-4-44-2-440000-442-2-222-222323−23−232323−23−2300000000002-2−2323−2323-220000000000000000000000000000000000000000000000000000
χ884-44-44-4-44-2-440000-442-2-222-22−23−232323−23−23232300000000002-223−2323−23-220000000000000000000000000000000000000000000000000000
χ894-44-4-444-4-2-4-444-4-44422-2-222-2-2-22222-2-2-4400000000222-2-22-2-20000000000000000000000000000000000000000000000000000
χ904-44-4-444-4-2-4-4-4-4444422-2-222-222-2-2-2-2224-40000000022-222-2-2-20000000000000000000000000000000000000000000000000000
χ914-4-444-44-44004-4-4400-4-4-4-44444-4-444-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-444-44-4400-444-400-4-4-4-4444-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ934-4-444-44-4-2004-4-44002222-2-2-2-222-2-222-2000000000000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000000000
χ944-4-444-44-4-2004-4-44002222-2-2-2-222-2-222-2000000000000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000000000
χ954-4-444-44-4-200-444-4002222-2-2-22-2-222-2-22000000000000000000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000000000
χ964-4-444-44-4-200-444-4002222-2-2-22-2-222-2-22000000000000000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000000000
χ974-4-44-44-44400000000-44-444-4-40000000000000022−22−22220000000000000000−222222−2222−22−2222000000000000000000000000000000000000
χ984-4-44-44-44400000000-44-444-4-400000000000000−222222−22000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ994-4-44-44-44-2000000002-22-2-22223−23−2323−232323−2300000022−22−222200000000−666−66−6−662−2−22−222−2000000000000000000000000000000000000
χ1004-4-44-44-44-2000000002-22-2-22223−23−2323−232323−23000000−222222−22000000006−6−66−666−6−222−22−2−22000000000000000000000000000000000000
χ1014-4-44-44-44-2000000002-22-2-222−232323−2323−23−232300000022−22−2222000000006−6−66−666−62−2−22−222−2000000000000000000000000000000000000
χ1024-4-44-44-44-2000000002-22-2-222−232323−2323−23−2323000000−222222−2200000000−666−66−6−66−222−22−2−22000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).