Finite Group Databasebeta

← Group #10825704

Character table — Group #10825704

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222223444444444444666666612121212121212121212121244444444888812121212121212121212121212121212242424242424242488888888444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-111-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-11
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11-1-11-1-1-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-11111-1
χ9111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-11
χ10111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-11111-1-111-1
χ11111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1-111111-1
χ12111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-111-1-1-1-1-11
χ13111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1
χ14111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-111111
χ15111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-1-111-1-1-1111
χ16111111111-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-1111-1-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000200-20020000-2
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000-200200-200002
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-22222-2-200000000000000000000000000000000000000000000200200-20000-2
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-22222-2-200000000000000000000000000000000000000000000-200-200200002
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2522222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ2622222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-122-2-2-2-222-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ2722222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1-2-22222-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ2822222222-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ292222-2-2-2-2222-2-22222-2-2-2-2-2-22-2-22222-2-22222-2-2-2-22-22-2000000000000000022-2-222-2-20000000000000000000000000000
χ302222-2-2-2-2222-2-22222-2-2-2-2-2-22-2-22222-2-22222-2-2-2-2-22-220000000000000000-2-222-2-2220000000000000000000000000000
χ312222-2-2-2-2222-2-2-2-2-2-22222-2-22-2-22222-2-2-2-2-2-222220000000000000000000000000000000000000000000002i−2i0000002i−2i0
χ322222-2-2-2-2222-2-2-2-2-2-22222-2-22-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000000000000−2i2i000000−2i2i0
χ332222-2-2-2-22-2-22222-2-222-2-2-2-22-2-222-2-22222-2-222-2-22-2-22000000000000000022-2-2-2-2220000000000000000000000000000
χ342222-2-2-2-22-2-22222-2-222-2-2-2-22-2-222-2-22222-2-222-2-2-222-20000000000000000-2-22222-2-20000000000000000000000000000
χ352222-2-2-2-22-2-222-2-222-2-222-2-22-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000000002i−2i000000−2i2i0
χ362222-2-2-2-22-2-222-2-222-2-222-2-22-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000−2i2i0000002i−2i0
χ372222-2-2-2-2-122-2-22222-2-2-2-211-111-1-1-1-111-1-1-1-111112-22-20000000033−3−333−3−3-1-111-1-11133−3−333−3−300000000000000000000
χ382222-2-2-2-2-122-2-22222-2-2-2-211-111-1-1-1-111-1-1-1-111112-22-200000000−3−333−3−333-1-111-1-111−3−333−3−33300000000000000000000
χ392222-2-2-2-2-122-2-22222-2-2-2-211-111-1-1-1-111-1-1-1-11111-22-220000000033−3−333−3−311-1-111-1-1−3−333−3−33300000000000000000000
χ402222-2-2-2-2-122-2-22222-2-2-2-211-111-1-1-1-111-1-1-1-11111-22-2200000000−3−333−3−33311-1-111-1-133−3−333−3−300000000000000000000
χ412222-2-2-2-2-1-2-22222-2-222-2-211-111-1-111-1-1-1-111-1-1112-2-220000000033−3−3−3−333-1-11111-1-133−3−3−3−33300000000000000000000
χ422222-2-2-2-2-1-2-22222-2-222-2-211-111-1-111-1-1-1-111-1-1112-2-2200000000−3−33333−3−3-1-11111-1-1−3−33333−3−300000000000000000000
χ432222-2-2-2-2-1-2-22222-2-222-2-211-111-1-111-1-1-1-111-1-111-222-20000000033−3−3−3−33311-1-1-1-111−3−33333−3−300000000000000000000
χ442222-2-2-2-2-1-2-22222-2-222-2-211-111-1-111-1-1-1-111-1-111-222-200000000−3−33333−3−311-1-1-1-11133−3−3−3−33300000000000000000000
χ452-22-22-2-2222i−2i2i−2i2-22i−2i2i−2i2-22-2-22-22-22i−2i2i−2i2-22i−2i2i−2i2-20000000000000000000000000000000000000000000000002i−2i02-2000
χ462-22-22-2-2222i−2i2i−2i2-22i−2i2i−2i2-22-2-22-22-22i−2i2i−2i2-22i−2i2i−2i2-2000000000000000000000000000000000000000000000000−2i2i0-22000
χ472-22-22-2-2222i−2i2i−2i-22−2i2i−2i2i-222-2-22-22-22i−2i2i−2i-22−2i2i−2i2i-2200002-22i−2i00002-22-22i−2i2i−2i000000000000000000000000000000000000
χ482-22-22-2-2222i−2i2i−2i-22−2i2i−2i2i-222-2-22-22-22i−2i2i−2i-22−2i2i−2i2i-220000-22−2i2i0000-22-22−2i2i−2i2i000000000000000000000000000000000000
χ492-22-22-2-222−2i2i−2i2i2-2−2i2i−2i2i2-22-2-22-22-2−2i2i−2i2i2-2−2i2i−2i2i2-20000000000000000000000000000000000000000000000002i−2i0-22000
χ502-22-22-2-222−2i2i−2i2i2-2−2i2i−2i2i2-22-2-22-22-2−2i2i−2i2i2-2−2i2i−2i2i2-2000000000000000000000000000000000000000000000000−2i2i02-2000
χ512-22-22-2-222−2i2i−2i2i-222i−2i2i−2i-222-2-22-22-2−2i2i−2i2i-222i−2i2i−2i-2200002-2−2i2i00002-22-2−2i2i−2i2i000000000000000000000000000000000000
χ522-22-22-2-222−2i2i−2i2i-222i−2i2i−2i-222-2-22-22-2−2i2i−2i2i-222i−2i2i−2i-220000-222i−2i0000-22-222i−2i2i−2i000000000000000000000000000000000000
χ532-22-22-2-22-12i−2i2i−2i-22−2i2i−2i2i-22-111-11-11−ii−ii1-1i−ii−i1-100002-22i−2i0000-11-11−ii−ii−i3i3−i3i33−33−3−i3i3−i3i33−33−300000000000000000000
χ542-22-22-2-22-12i−2i2i−2i-22−2i2i−2i2i-22-111-11-11−ii−ii1-1i−ii−i1-100002-22i−2i0000-11-11−ii−iii3−i3i3−i3−33−33i3−i3i3−i3−33−3300000000000000000000
χ552-22-22-2-22-12i−2i2i−2i-22−2i2i−2i2i-22-111-11-11−ii−ii1-1i−ii−i1-10000-22−2i2i00001-11-1i−ii−i−i3i3−i3i33−33−3i3−i3i3−i3−33−3300000000000000000000
χ562-22-22-2-22-12i−2i2i−2i-22−2i2i−2i2i-22-111-11-11−ii−ii1-1i−ii−i1-10000-22−2i2i00001-11-1i−ii−ii3−i3i3−i3−33−33−i3i3−i3i33−33−300000000000000000000
χ572-22-22-2-22-1−2i2i−2i2i-222i−2i2i−2i-22-111-11-11i−ii−i1-1−ii−ii1-100002-2−2i2i0000-11-11i−ii−i−i3i3−i3i3−33−33−i3i3−i3i3−33−3300000000000000000000
χ582-22-22-2-22-1−2i2i−2i2i-222i−2i2i−2i-22-111-11-11i−ii−i1-1−ii−ii1-100002-2−2i2i0000-11-11i−ii−ii3−i3i3−i33−33−3i3−i3i3−i33−33−300000000000000000000
χ592-22-22-2-22-1−2i2i−2i2i-222i−2i2i−2i-22-111-11-11i−ii−i1-1−ii−ii1-10000-222i−2i00001-11-1−ii−ii−i3i3−i3i3−33−33i3−i3i3−i33−33−300000000000000000000
χ602-22-22-2-22-1−2i2i−2i2i-222i−2i2i−2i-22-111-11-11i−ii−i1-1−ii−ii1-10000-222i−2i00001-11-1−ii−iii3−i3i3−i33−33−3−i3i3−i3i3−33−3300000000000000000000
χ612-22-2-222-222i−2i−2i2i2-22i−2i−2i2i-22-22-2-222-22i−2i−2i2i2-22i−2i−2i2i-220000000000000000000000000000000000002i2i−2i−2i22-2-2000000000000
χ622-22-2-222-222i−2i−2i2i2-22i−2i−2i2i-22-22-2-222-22i−2i−2i2i2-22i−2i−2i2i-22000000000000000000000000000000000000−2i−2i2i2i-2-222000000000000
χ632-22-2-222-222i−2i−2i2i-22−2i2i2i−2i2-2-22-2-222-22i−2i−2i2i-22−2i2i2i−2i2-2000000002i−2i2-200000000000000002i−2i−2i2i-222-200000000000000000000
χ642-22-2-222-222i−2i−2i2i-22−2i2i2i−2i2-2-22-2-222-22i−2i−2i2i-22−2i2i2i−2i2-200000000−2i2i-220000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ652-22-2-222-22−2i2i2i−2i2-2−2i2i2i−2i-22-22-2-222-2−2i2i2i−2i2-2−2i2i2i−2i-220000000000000000000000000000000000002i2i−2i−2i-2-222000000000000
χ662-22-2-222-22−2i2i2i−2i2-2−2i2i2i−2i-22-22-2-222-2−2i2i2i−2i2-2−2i2i2i−2i-22000000000000000000000000000000000000−2i−2i2i2i22-2-2000000000000
χ672-22-2-222-22−2i2i2i−2i-222i−2i−2i2i2-2-22-2-222-2−2i2i2i−2i-222i−2i−2i2i2-2000000002i−2i-2200000000000000002i−2i−2i2i2-2-2200000000000000000000
χ682-22-2-222-22−2i2i2i−2i-222i−2i−2i2i2-2-22-2-222-2−2i2i2i−2i-222i−2i−2i2i2-200000000−2i2i2-20000000000000000−2i2i2i−2i-222-200000000000000000000
χ692-22-2-222-2-12i−2i−2i2i-22−2i2i2i−2i2-21-111-1-11−iii−i1-1i−i−ii-11000000002i−2i2-23−3−33i3−i3−i3i3−i3i3i3−i33−3−33−iii−i1-1-1100000000000000000000
χ702-22-2-222-2-12i−2i−2i2i-22−2i2i2i−2i2-21-111-1-11−iii−i1-1i−i−ii-11000000002i−2i2-2−333−3−i3i3i3−i3i3−i3−i3i3−333−3−iii−i1-1-1100000000000000000000
χ712-22-2-222-2-12i−2i−2i2i-22−2i2i2i−2i2-21-111-1-11−iii−i1-1i−i−ii-1100000000−2i2i-223−3−33i3−i3−i3i3i3−i3−i3i3−333−3i−i−ii-111-100000000000000000000
χ722-22-2-222-2-12i−2i−2i2i-22−2i2i2i−2i2-21-111-1-11−iii−i1-1i−i−ii-1100000000−2i2i-22−333−3−i3i3i3−i3−i3i3i3−i33−3−33i−i−ii-111-100000000000000000000
χ732-22-2-222-2-1−2i2i2i−2i-222i−2i−2i2i2-21-111-1-11i−i−ii1-1−iii−i-11000000002i−2i-223−3−33−i3i3i3−i3−i3i3i3−i3−333−3−iii−i-111-100000000000000000000
χ742-22-2-222-2-1−2i2i2i−2i-222i−2i−2i2i2-21-111-1-11i−i−ii1-1−iii−i-11000000002i−2i-22−333−3i3−i3−i3i3i3−i3−i3i33−3−33−iii−i-111-100000000000000000000
χ752-22-2-222-2-1−2i2i2i−2i-222i−2i−2i2i2-21-111-1-11i−i−ii1-1−iii−i-1100000000−2i2i2-23−3−33−i3i3i3−i3i3−i3−i3i33−3−33i−i−ii1-1-1100000000000000000000
χ762-22-2-222-2-1−2i2i2i−2i-222i−2i−2i2i2-21-111-1-11i−i−ii1-1−iii−i-1100000000−2i2i2-2−333−3i3−i3−i3i3−i3i3i3−i3−333−3i−i−ii1-1-1100000000000000000000
χ7744444444-24444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-4-4-44444-4-4-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-4-244-4-4-4-4-4-4444422-222-2-2-2-2222222-2-2-2-200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-2-4-444-4-444-4-44422-222-2-222-2-222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ8144-4-444-4-44000000000000-4444-4-4-400000000000000000000000000000000000000000000000022−2222−220000000000000000
χ8244-4-444-4-44000000000000-4444-4-4-4000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ8344-4-4-4-44440000000000004-44-44-4-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ8444-4-4-4-44440000000000004-44-44-4-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ854-44-44-4-44-24i−4i4i−4i4-44i−4i4i−4i4-4-222-22-22−2i2i−2i2i-22−2i2i−2i2i-2200000000000000000000000000000000000000000000000000000000
χ864-44-44-4-44-2−4i4i−4i4i4-4−4i4i−4i4i4-4-222-22-222i−2i2i−2i-222i−2i2i−2i-2200000000000000000000000000000000000000000000000000000000
χ874-44-4-444-4-24i−4i−4i4i4-44i−4i−4i4i-442-222-2-22−2i2i2i−2i-22−2i2i2i−2i2-200000000000000000000000000000000000000000000000000000000
χ884-44-4-444-4-2−4i4i4i−4i4-4−4i4i4i−4i-442-222-2-222i−2i−2i2i-222i−2i−2i2i2-200000000000000000000000000000000000000000000000000000000
χ894-4-444-44-44000000000000-4-4-444-440000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ904-4-444-44-44000000000000-4-4-444-4400000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ914-4-44-44-44400000000000044-4-4-4-44000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ924-4-44-44-44400000000000044-4-4-4-440000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ9388-8-888-8-8-40000000000004-4-4-444400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-8-888-4000000000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888-88-8-4000000000000444-4-44-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-88-88-4000000000000-4-44444-400000000000000000000000000000000000000000000000000000000000000000000

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