Finite Group Databasebeta

← Group #10702172

Character table — Group #10702172

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12222222222234444444466666666666121212121212121244448888888812121212121212122424242424242424242424242424242444444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911-1-11-1-111-1-1111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i11-1-1
χ1011-1-11-1-111-1-1111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii-1-111
χ1111-1-11-1-111-1-1111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii11-1-1
χ1211-1-11-1-111-1-1111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i-1-111
χ1311-1-11-1-111-1-1111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i−i−iii-1-111
χ1411-1-11-1-111-1-1111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−i11-1-1
χ1511-1-11-1-111-1-1111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iiiii−i−i-1-111
χ1611-1-11-1-111-1-1111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iii11-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-22-22-20000000022-2-222-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-22-2200000000-2-222-2-222000000000000000000000000000000000000
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
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-22-200000000-1-111-1-11133−3−333−3−333−3−333−3−300000000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-22-200000000-1-111-1-111−3−333−3−333−3−333−3−33300000000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-22-220000000011-1-111-1-133−3−333−3−3−3−333−3−33300000000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-22-220000000011-1-111-1-1−3−333−3−33333−3−333−3−300000000000000000000
χ2722222222-2-2-2-2222-2-22-22-22222222-2-2-2-222-2-22-22-20000000000000000000000000000000000000000000000002-22-20000
χ2822222222-2-2-2-2222-2-22-22-22222222-2-2-2-222-2-22-22-2000000000000000000000000000000000000000000000000-22-220000
χ2922222222-2-2-2-22-2-222-22-222222222-2-2-2-2-2-222-22-22000000000000000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-22-2-222-22-222222222-2-2-2-2-2-222-22-2200000000000000000000000000000000000000000000-22-2200000000
χ3122-2-22-2-222-2-222-2-2-2-222222-2-2-2-22222-2-2-2-2-2-222222-2-220000000022-2-2-2-222000000000000000000000000000000000000
χ3222-2-22-2-222-2-222-2-2-2-222222-2-2-2-22222-2-2-2-2-2-22222-222-200000000-2-22222-2-2000000000000000000000000000000000000
χ3322-2-22-2-222-2-22-12222-2-2-2-2-11111-1-1-1-111-1-1-1-1111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ3422-2-22-2-222-2-22-12222-2-2-2-2-11111-1-1-1-111-1-1-1-1111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ3522-2-22-2-222-2-22-12222-2-2-2-2-11111-1-1-1-111-1-1-1-11111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ3622-2-22-2-222-2-22-12222-2-2-2-2-11111-1-1-1-111-1-1-1-11111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ3722-2-22-2-222-2-22-1-2-2-2-22222-11111-1-1-1-1111111-1-1-1-12-2-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3822-2-22-2-222-2-22-1-2-2-2-22222-11111-1-1-1-1111111-1-1-1-12-2-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3922-2-22-2-222-2-22-1-2-2-2-22222-11111-1-1-1-1111111-1-1-1-1-222-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ4022-2-22-2-222-2-22-1-2-2-2-22222-11111-1-1-1-1111111-1-1-1-1-222-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ4122-2-22-2-22-222-2222-2-2-22-222-2-2-2-222-2-22222-2-2-22-220000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ4222-2-22-2-22-222-2222-2-2-22-222-2-2-2-222-2-22222-2-2-22-22000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ4322-2-22-2-22-222-22-2-2222-22-22-2-2-2-222-2-222-2-2222-22-2000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ4422-2-22-2-22-222-22-2-2222-22-22-2-2-2-222-2-222-2-2222-22-200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ452-222-2-2-2222-2-222-22-222-2-2-222-2-22-22-22-22-22-222-2-200000000000000000000000000000000000000000000000000002-22-2
χ462-222-2-2-2222-2-222-22-222-2-2-222-2-22-22-22-22-22-222-2-20000000000000000000000000000000000000000000000000000-22-22
χ472-222-2-2-2222-2-22-22-22-2-222-222-2-22-22-22-2-22-22-2-2220000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ482-222-2-2-2222-2-22-22-22-2-222-222-2-22-22-22-2-22-22-2-222000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ492-222-2-2-22-2-22222-2-222-2-22-222-2-22-2-22-222-2-222-2-2200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ502-222-2-2-22-2-22222-2-222-2-22-222-2-22-2-22-222-2-222-2-220000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ512-222-2-2-22-2-2222-222-2-222-2-222-2-22-2-22-22-222-2-222-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ522-222-2-2-22-2-2222-222-2-222-2-222-2-22-2-22-22-222-2-222-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ532-222-2-2-22-2-222-12-2-222-2-221-1-111-111-11-1-111-1-111-100002i−2i2i−2i00003−33−33−33−3−ii−ii−ii−ii−i3i3i3−i3−i3i3i3−i300000000000000000000
χ542-222-2-2-22-2-222-12-2-222-2-221-1-111-111-11-1-111-1-111-100002i−2i2i−2i0000−33−33−33−33−ii−ii−ii−iii3−i3−i3i3i3−i3−i3i300000000000000000000
χ552-222-2-2-22-2-222-12-2-222-2-221-1-111-111-11-1-111-1-111-10000−2i2i−2i2i00003−33−33−33−3i−ii−ii−ii−ii3−i3−i3i3i3−i3−i3i300000000000000000000
χ562-222-2-2-22-2-222-12-2-222-2-221-1-111-111-11-1-111-1-111-10000−2i2i−2i2i0000−33−33−33−33i−ii−ii−ii−i−i3i3i3−i3−i3i3i3−i300000000000000000000
χ572-222-2-2-22-2-222-1-222-2-222-21-1-111-111-11-11-1-111-1-11000000002i−2i2i−2i3−3−333−3−33i3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii00000000000000000000
χ582-222-2-2-22-2-222-1-222-2-222-21-1-111-111-11-11-1-111-1-11000000002i−2i2i−2i−333−3−333−3−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii00000000000000000000
χ592-222-2-2-22-2-222-1-222-2-222-21-1-111-111-11-11-1-111-1-1100000000−2i2i−2i2i3−3−333−3−33−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i00000000000000000000
χ602-222-2-2-22-2-222-1-222-2-222-21-1-111-111-11-11-1-111-1-1100000000−2i2i−2i2i−333−3−333−3i3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i00000000000000000000
χ612-2-2-2-22222-22-222-22-2-2-222-2-2-2222-22-2-222-22-2-2-22200000000000000000000000000000000000000000000000000002-2-22
χ622-2-2-2-22222-22-222-22-2-2-222-2-2-2222-22-2-222-22-2-2-2220000000000000000000000000000000000000000000000000000-222-2
χ632-2-2-2-22222-22-22-22-2222-2-2-2-2-2222-22-2-22-22-2222-2-20000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ642-2-2-2-22222-22-22-22-2222-2-2-2-2-2222-22-2-22-22-2222-2-2000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ652-2-2-2-2222-22-2222-2-22-222-2-2-2-2222-2-222-22-2-22-222-200002-2-220000000000002-22-2-22-220000000000000000000000000000
χ662-2-2-2-2222-22-2222-2-22-222-2-2-2-2222-2-222-22-2-22-222-20000-222-2000000000000-22-222-22-20000000000000000000000000000
χ672-2-2-2-2222-22-222-222-22-2-22-2-2-2222-2-222-2-222-22-2-22000000002-2-2200000000000000002-22-2-22-2200000000000000000000
χ682-2-2-2-2222-22-222-222-22-2-22-2-2-2222-2-222-2-222-22-2-2200000000-222-20000000000000000-22-222-22-200000000000000000000
χ692-2-2-2-2222-22-22-12-2-22-222-2111-1-1-111-1-11-111-11-1-1100002-2-2200003−33−3−33−33-11-111-11-1−333−33−3−3300000000000000000000
χ702-2-2-2-2222-22-22-12-2-22-222-2111-1-1-111-1-11-111-11-1-1100002-2-220000−33−333−33−3-11-111-11-13−3−33−333−300000000000000000000
χ712-2-2-2-2222-22-22-12-2-22-222-2111-1-1-111-1-11-111-11-1-110000-222-200003−33−3−33−331-11-1-11-113−3−33−333−300000000000000000000
χ722-2-2-2-2222-22-22-12-2-22-222-2111-1-1-111-1-11-111-11-1-110000-222-20000−33−333−33−31-11-1-11-11−333−33−3−3300000000000000000000
χ732-2-2-2-2222-22-22-1-222-22-2-22111-1-1-111-1-111-1-11-111-1000000002-2-223−3−33−333−33−3−33−333−3-11-111-11-100000000000000000000
χ742-2-2-2-2222-22-22-1-222-22-2-22111-1-1-111-1-111-1-11-111-1000000002-2-22−333−33−3−33−333−33−3−33-11-111-11-100000000000000000000
χ752-2-2-2-2222-22-22-1-222-22-2-22111-1-1-111-1-111-1-11-111-100000000-222-23−3−33−333−3−333−33−3−331-11-1-11-1100000000000000000000
χ762-2-2-2-2222-22-22-1-222-22-2-22111-1-1-111-1-111-1-11-111-100000000-222-2−333−33−3−333−3−33−333−31-11-1-11-1100000000000000000000
χ7744444444-4-4-4-4-244-4-44-44-4-2-2-2-2-2-2-22222-2-222-22-2200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-2-4-444-44-44-2-2-2-2-2-2-2222222-2-22-22-200000000000000000000000000000000000000000000000000000000
χ79444-4-44-4-4000040000000044-44-4-4-40000000000000000000000000000000000000000000000002-22-22-22-2000000000000
χ80444-4-44-4-4000040000000044-44-4-4-4000000000000000000000000000000000000000000000000-22-22-22-22000000000000
χ8144-44-4-44-400004000000004-44-44-4-40000000000000000000000000000000000000000000000002-22-2-22-22000000000000
χ8244-44-4-44-400004000000004-44-44-4-4000000000000000000000000000000000000000000000000-22-222-22-2000000000000
χ8344-4-44-4-44-444-4-244-4-4-44-44-22222-2-222-2-2-2-2222-22-200000000000000000000000000000000000000000000000000000000
χ8444-4-44-4-44-444-4-2-4-4444-44-4-22222-2-222-2-222-2-2-22-2200000000000000000000000000000000000000000000000000000000
χ854-444-4-4-4444-4-4-24-44-444-4-42-2-222-22-22-22-22-22-2-22200000000000000000000000000000000000000000000000000000000
χ864-444-4-4-4444-4-4-2-44-44-4-4442-2-222-22-22-222-22-222-2-200000000000000000000000000000000000000000000000000000000
χ874-44-44-44-40000400000000-44-4-44-440000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ884-44-44-44-40000400000000-44-4-44-44000000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ894-4-4444-4-40000400000000-4-444-4-440000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ904-4-4444-4-40000400000000-4-444-4-44000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ914-4-4-4-44444-44-4-24-44-4-4-444222-2-2-22-222-2-22-2222-2-200000000000000000000000000000000000000000000000000000000
χ924-4-4-4-44444-44-4-2-44-4444-4-4222-2-2-22-222-22-22-2-2-22200000000000000000000000000000000000000000000000000000000
χ93888-8-88-8-80000-400000000-4-44-444400000000000000000000000000000000000000000000000000000000000000000000
χ9488-88-8-88-80000-400000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ958-88-88-88-80000-4000000004-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8888-8-80000-40000000044-4-444-400000000000000000000000000000000000000000000000000000000000000000000

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