Finite Group Databasebeta

← Group #10823176

Character table — Group #10823176

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12222222222234444444466666666666121212121212121244444444888812121212121212121212121212121212242424242424242488888888222222444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ911111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1
χ1011111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1
χ1211111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ1311111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ1411111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1
χ1511111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1611111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000002-22-200
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000-22-2200
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2322222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-22222-2000000000000000000000000000000000000000000000000002-2-2200
χ2422222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-22222-200000000000000000000000000000000000000000000000000-222-200
χ2522222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-11111-122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ2622222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-11111-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ2722222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-11111-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ2822222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-11111-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ2922-2-22-2-2222-2-2222-222-2-2-22-2-22-2-2222-2-222-222-2-2-22i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ3022-2-22-2-2222-2-2222-222-2-2-22-2-22-2-2222-2-222-222-2-2-2−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3122-2-22-2-2222-2-22-2-22-2-22222-2-22-2-2222-2-2-2-22-2-222200000000000000000000000000000000000000000000002-22-2000000
χ3222-2-22-2-2222-2-22-2-22-2-22222-2-22-2-2222-2-2-2-22-2-22220000000000000000000000000000000000000000000000-22-22000000
χ3322-2-22-2-2222-2-2-122-222-2-2-2-111-111-1-1-111-1-11-1-11112i−2i2i−2i00000000−i−iii−i−iii−i3−i3i3i3−i3−i3i3i333−3−333−3−300000000000000000000
χ3422-2-22-2-2222-2-2-122-222-2-2-2-111-111-1-1-111-1-11-1-11112i−2i2i−2i00000000−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3−3−333−3−33300000000000000000000
χ3522-2-22-2-2222-2-2-122-222-2-2-2-111-111-1-1-111-1-11-1-1111−2i2i−2i2i00000000ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3−3−333−3−33300000000000000000000
χ3622-2-22-2-2222-2-2-122-222-2-2-2-111-111-1-1-111-1-11-1-1111−2i2i−2i2i00000000ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i333−3−333−3−300000000000000000000
χ3722-2-22-2-22-2-222222-2-2-222-22-2-22-2-22-2-22222-2-2-222-22i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ3822-2-22-2-22-2-222222-2-2-222-22-2-22-2-22-2-22222-2-2-222-2−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ3922-2-22-2-22-2-2222-2-2222-2-222-2-22-2-22-2-222-2-2222-2-2200000000000000000000000000000000000000000000002-2-22000000
χ4022-2-22-2-22-2-2222-2-2222-2-222-2-22-2-22-2-222-2-2222-2-220000000000000000000000000000000000000000000000-222-2000000
χ4122-2-22-2-22-2-222-122-2-2-222-2-111-111-111-1-1-1-1111-1-112i−2i−2i2i00000000−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i333−3−3−3−33300000000000000000000
χ4222-2-22-2-22-2-222-122-2-2-222-2-111-111-111-1-1-1-1111-1-112i−2i−2i2i00000000−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i3−3−33333−3−300000000000000000000
χ4322-2-22-2-22-2-222-122-2-2-222-2-111-111-111-1-1-1-1111-1-11−2i2i2i−2i00000000ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i3−3−33333−3−300000000000000000000
χ4422-2-22-2-22-2-222-122-2-2-222-2-111-111-111-1-1-1-1111-1-11−2i2i2i−2i00000000ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i333−3−3−3−33300000000000000000000
χ452-222-2-2-222-22-222-222-22-2-2-2-2-2222-22-22-22-222-22-2-200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ462-222-2-2-222-22-222-222-22-2-2-2-2-2222-22-22-22-222-22-2-20000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ472-222-2-2-222-22-22-22-2-22-222-2-2-2222-22-22-2-22-2-22-222000000000000000000000000000000000000000000002-2000000002-2
χ482-222-2-2-222-22-22-22-2-22-222-2-2-2222-22-22-2-22-2-22-22200000000000000000000000000000000000000000000-2200000000-22
χ492-222-2-2-222-22-2-12-222-22-2-2111-1-1-11-11-11-11-1-11-11100002i−2i2i−2i0000−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii3−33−33−33−300000000000000000000
χ502-222-2-2-222-22-2-12-222-22-2-2111-1-1-11-11-11-11-1-11-11100002i−2i2i−2i0000i3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii−33−33−33−3300000000000000000000
χ512-222-2-2-222-22-2-12-222-22-2-2111-1-1-11-11-11-11-1-11-1110000−2i2i−2i2i0000−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i−33−33−33−3300000000000000000000
χ522-222-2-2-222-22-2-12-222-22-2-2111-1-1-11-11-11-11-1-11-1110000−2i2i−2i2i0000i3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i3−33−33−33−300000000000000000000
χ532-222-2-2-22-22-2222-22-22-22-2-2-2-2222-2-22-222-22-22-22-200002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ542-222-2-2-22-22-2222-22-22-22-2-2-2-2222-2-22-222-22-22-22-20000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ552-222-2-2-22-22-222-22-22-22-22-2-2-2222-2-22-22-22-22-22-22000000000000000000000000000000000000000000002-200000000-22
χ562-222-2-2-22-22-222-22-22-22-22-2-2-2222-2-22-22-22-22-22-2200000000000000000000000000000000000000000000-22000000002-2
χ572-222-2-2-22-22-22-12-22-22-22-2111-1-1-111-11-1-11-11-11-1100002i−2i−2i2i0000−i3i3−i3i3i3−i3i3−i3−ii−iii−ii−i3−33−3−33−3300000000000000000000
χ582-222-2-2-22-22-22-12-22-22-22-2111-1-1-111-11-1-11-11-11-1100002i−2i−2i2i0000i3−i3i3−i3−i3i3−i3i3−ii−iii−ii−i−33−333−33−300000000000000000000
χ592-222-2-2-22-22-22-12-22-22-22-2111-1-1-111-11-1-11-11-11-110000−2i2i2i−2i0000−i3i3−i3i3i3−i3i3−i3i−ii−i−ii−ii−33−333−33−300000000000000000000
χ602-222-2-2-22-22-22-12-22-22-22-2111-1-1-111-11-1-11-11-11-110000−2i2i2i−2i0000i3−i3i3−i3−i3i3−i3i3i−ii−i−ii−ii3−33−3−33−3300000000000000000000
χ612-2-2-2-22222-2-2222-2-22-2-222-2222-2-2-22-2-222-2-22-2-222000000002-22-200000000000000002-2-222-2-2200000000000000000000
χ622-2-2-2-22222-2-2222-2-22-2-222-2222-2-2-22-2-222-2-22-2-22200000000-22-220000000000000000-222-2-222-200000000000000000000
χ632-2-2-2-22222-2-222-222-222-2-2-2222-2-2-22-2-22-222-222-2-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ642-2-2-2-22222-2-222-222-222-2-2-2222-2-2-22-2-22-222-222-2-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ652-2-2-2-22222-2-22-12-2-22-2-2221-1-1-1111-111-1-111-111-1-1000000002-22-23−3−333−3−33−333−3−333−3-111-1-111-100000000000000000000
χ662-2-2-2-22222-2-22-12-2-22-2-2221-1-1-1111-111-1-111-111-1-1000000002-22-2−333−3−333−33−3−333−3−33-111-1-111-100000000000000000000
χ672-2-2-2-22222-2-22-12-2-22-2-2221-1-1-1111-111-1-111-111-1-100000000-22-223−3−333−3−333−3−333−3−331-1-111-1-1100000000000000000000
χ682-2-2-2-22222-2-22-12-2-22-2-2221-1-1-1111-111-1-111-111-1-100000000-22-22−333−3−333−3−333−3−333−31-1-111-1-1100000000000000000000
χ692-2-2-2-2222-222-222-2-2-222-22-2222-2-2-2-222-22-2-2-222-22000000002-2-2200000000000000002-2-22-222-200000000000000000000
χ702-2-2-2-2222-222-222-2-2-222-22-2222-2-2-2-222-22-2-2-222-2200000000-222-20000000000000000-222-22-2-2200000000000000000000
χ712-2-2-2-2222-222-22-2222-2-22-2-2222-2-2-2-222-2-2222-2-22-20000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ722-2-2-2-2222-222-22-2222-2-22-2-2222-2-2-2-222-2-2222-2-22-2000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ732-2-2-2-2222-222-2-12-2-2-222-221-1-1-11111-1-11-1111-1-11-1000000002-2-223−3−33−333−3−333−33−3−33-111-11-1-1100000000000000000000
χ742-2-2-2-2222-222-2-12-2-2-222-221-1-1-11111-1-11-1111-1-11-1000000002-2-22−333−33−3−333−3−33−333−3-111-11-1-1100000000000000000000
χ752-2-2-2-2222-222-2-12-2-2-222-221-1-1-11111-1-11-1111-1-11-100000000-222-23−3−33−333−33−3−33−333−31-1-11-111-100000000000000000000
χ762-2-2-2-2222-222-2-12-2-2-222-221-1-1-11111-1-11-1111-1-11-100000000-222-2−333−33−3−33−333−33−3−331-1-11-111-100000000000000000000
χ77444444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-2-4-4-44444-4-2-2-2-2-2-2-22222222-2-2-2-2200000000000000000000000000000000000000000000000000000000
χ79444-4-44-4-4000040000000044-4-44-4-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ80444-4-44-4-4000040000000044-4-44-4-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ8144-44-4-44-400004000000004-44-4-44-4000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ8244-44-4-44-400004000000004-44-4-44-40000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ8344-4-44-4-4444-4-4-2-4-44-4-4444-222-222-2-2-22222-222-2-2-200000000000000000000000000000000000000000000000000000000
χ8444-4-44-4-44-4-444-2-4-4444-4-44-222-222-222-2-222-2-2-222-200000000000000000000000000000000000000000000000000000000
χ854-444-4-4-444-44-4-2-44-4-44-444222-2-2-22-22-222-222-22-2-200000000000000000000000000000000000000000000000000000000
χ864-444-4-4-44-44-44-2-44-44-44-44222-2-2-222-22-22-22-22-22-200000000000000000000000000000000000000000000000000000000
χ874-44-44-44-40000400000000-4-44-44-4400000000000000000000000000000000000000000000000022−22−22220000000000000000
χ884-44-44-44-40000400000000-4-44-44-44000000000000000000000000000000000000000000000000−222222−220000000000000000
χ894-4-4444-4-40000400000000-44-4-4-444000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ904-4-4444-4-40000400000000-44-4-4-4440000000000000000000000000000000000000000000000000000−222222−22000000000000
χ914-4-4-4-44444-4-44-2-444-444-4-42-2-2-2222-222-22-2-22-2-22200000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-444-4-2-4444-4-44-42-2-2-22222-2-222-2-2-222-2200000000000000000000000000000000000000000000000000000000
χ93888-8-88-8-80000-400000000-4-444-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-88-8-88-80000-400000000-44-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ958-88-88-88-80000-40000000044-44-44-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8888-8-80000-4000000004-4444-4-400000000000000000000000000000000000000000000000000000000000000000000

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