Finite Group Databasebeta

← Group #10801771

Character table — Group #10801771

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222224444444444444444666666666666666688888888888888888888121212121212121216161616161616162424242424242424
order1222222234444666666644448888888812121212222244444444444422444444121212122424242424242424888888886612121212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111
χ911111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1
χ171-11-11-11-111-11-11-11-11-1-1i−ii−i11-1-1ii−i−i1-11-111-1-1ii−i−i11-1-1ii−i−i1-11-1i−ii−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ181-11-11-11-111-11-11-11-11-1-1i−ii−i11-1-1ii−i−i1-11-111-1-1ii−i−i11-1-1ii−i−i-11-11−ii−iii−ii−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii-11−ii
χ191-11-11-11-111-11-11-11-11-1-1i−ii−i11-1-1ii−i−i1-11-1-1-111−i−iii-1-111−i−iii1-11-1i−ii−ii−ii−i11-1-1ii−i−i-1-111−i−iii1-1i−i1-1i−i-11−ii-11−ii
χ201-11-11-11-111-11-11-11-11-1-1i−ii−i11-1-1ii−i−i1-11-1-1-111−i−iii-1-111−i−iii-11-11−ii−iii−ii−i11-1-1ii−i−i-1-111−i−iii-11−ii-11−ii1-1i−i1-1i−i
χ211-11-11-11-111-11-11-11-11-1-1i−ii−i-1-111−i−iii1-11-111-1-1ii−i−i11-1-1ii−i−i1-1-11i−i−iii−ii−i-1-111−i−iii-1-111−i−iii1-1i−i-11−ii1-1−ii-11i−i
χ221-11-11-11-111-11-11-11-11-1-1i−ii−i-1-111−i−iii1-11-111-1-1ii−i−i11-1-1ii−i−i-111-1−iii−ii−ii−i-1-111−i−iii-1-111−i−iii-11−ii1-1i−i-11i−i1-1−ii
χ231-11-11-11-111-11-11-11-11-1-1i−ii−i-1-111−i−iii1-11-1-1-111−i−iii-1-111−i−iii1-1-11i−i−iii−ii−i-1-111−i−iii11-1-1ii−i−i1-1i−i-11−ii-11i−i1-1−ii
χ241-11-11-11-111-11-11-11-11-1-1i−ii−i-1-111−i−iii1-11-1-1-111−i−iii-1-111−i−iii-111-1−iii−ii−ii−i-1-111−i−iii11-1-1ii−i−i-11−ii1-1i−i1-1−ii-11i−i
χ251-11-11-11-111-11-11-11-11-1-1−ii−ii11-1-1−i−iii1-11-111-1-1−i−iii11-1-1−i−iii1-11-1−ii−ii−ii−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii1-1−ii
χ261-11-11-11-111-11-11-11-11-1-1−ii−ii11-1-1−i−iii1-11-111-1-1−i−iii11-1-1−i−iii-11-11i−ii−i−ii−ii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i-11i−i
χ271-11-11-11-111-11-11-11-11-1-1−ii−ii11-1-1−i−iii1-11-1-1-111ii−i−i-1-111ii−i−i1-11-1−ii−ii−ii−ii11-1-1−i−iii-1-111ii−i−i1-1−ii1-1−ii-11i−i-11i−i
χ281-11-11-11-111-11-11-11-11-1-1−ii−ii11-1-1−i−iii1-11-1-1-111ii−i−i-1-111ii−i−i-11-11i−ii−i−ii−ii11-1-1−i−iii-1-111ii−i−i-11i−i-11i−i1-1−ii1-1−ii
χ291-11-11-11-111-11-11-11-11-1-1−ii−ii-1-111ii−i−i1-11-111-1-1−i−iii11-1-1−i−iii1-1-11−iii−i−ii−ii-1-111ii−i−i-1-111ii−i−i1-1−ii-11i−i1-1i−i-11−ii
χ301-11-11-11-111-11-11-11-11-1-1−ii−ii-1-111ii−i−i1-11-111-1-1−i−iii11-1-1−i−iii-111-1i−i−ii−ii−ii-1-111ii−i−i-1-111ii−i−i-11i−i1-1−ii-11−ii1-1i−i
χ311-11-11-11-111-11-11-11-11-1-1−ii−ii-1-111ii−i−i1-11-1-1-111ii−i−i-1-111ii−i−i1-1-11−iii−i−ii−ii-1-111ii−i−i11-1-1−i−iii1-1−ii-11i−i-11−ii1-1i−i
χ321-11-11-11-111-11-11-11-11-1-1−ii−ii-1-111ii−i−i1-11-1-1-111ii−i−i-1-111ii−i−i-111-1i−i−ii−ii−ii-1-111ii−i−i11-1-1−i−iii-11i−i1-1−ii1-1i−i-11−ii
χ33222222222-2-2-2-2222222222-2-200000000-2-2-2-222222222-2-2-2-2-2-2-2-20000000022-2-200000000000000000000000000000000
χ34222222222-2-2-2-2222222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2222222220000000022-2-200000000000000000000000000000000
χ35222222222-2-2-2-22222222-2-22200000000-2-2-2-22222-2-2-2-2-2-2-2-2222200000000-2-22200000000000000000000000000000000
χ36222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-2-2-222222222-2-2-2-200000000-2-22200000000000000000000000000000000
χ3722222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-100000000
χ3822222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-10000000000000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1000000001111111100000000
χ3922222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1000000000000000022-2-222-2-2-1-1-1-11111111100000000-1-1-1-1111100000000
χ4022222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-10000000000000000-2-222-2-222-1-1-1-111111111000000001111-1-1-1-100000000
χ4122222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-100000000000000002222-2-2-2-21111-1-1-1-1111100000000-1-111-1-11100000000
χ4222222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-10000000000000000-2-2-2-222221111-1-1-1-111110000000011-1-111-1-100000000
χ4322222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1000000000000000022-2-2-2-22211111111-1-1-1-100000000-1-11111-1-100000000
χ4422222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-10000000000000000-2-22222-2-211111111-1-1-1-10000000011-1-1-1-11100000000
χ4522-2-2-222-222-2-22-222-2-22-200002i−2i2i−2i00002-2-2200002i−2i2i−2i00002i−2i2i−2i0000000000002i−2i2i−2i000000002-22-20000000000000000
χ4622-2-2-222-222-2-22-222-2-22-200002i−2i2i−2i00002-2-220000−2i2i−2i2i0000−2i2i−2i2i0000000000002i−2i2i−2i00000000-22-220000000000000000
χ4722-2-2-222-222-2-22-222-2-22-20000−2i2i−2i2i00002-2-2200002i−2i2i−2i00002i−2i2i−2i000000000000−2i2i−2i2i00000000-22-220000000000000000
χ4822-2-2-222-222-2-22-222-2-22-20000−2i2i−2i2i00002-2-220000−2i2i−2i2i0000−2i2i−2i2i000000000000−2i2i−2i2i000000002-22-20000000000000000
χ4922-2-2-222-22-222-2-222-2-22-2000000002i−2i2i−2i-222-200002i−2i2i−2i0000−2i2i−2i2i00000000000000002i−2i2i−2i2-22-200000000000000000000
χ5022-2-2-222-22-222-2-222-2-22-2000000002i−2i2i−2i-222-20000−2i2i−2i2i00002i−2i2i−2i00000000000000002i−2i2i−2i-22-2200000000000000000000
χ5122-2-2-222-22-222-2-222-2-22-200000000−2i2i−2i2i-222-200002i−2i2i−2i0000−2i2i−2i2i0000000000000000−2i2i−2i2i-22-2200000000000000000000
χ5222-2-2-222-22-222-2-222-2-22-200000000−2i2i−2i2i-222-20000−2i2i−2i2i00002i−2i2i−2i0000000000000000−2i2i−2i2i2-22-200000000000000000000
χ532-22-22-22-22-22-222-22-22-2-22i−2i−2i2i00000000-22-2222-2-22i2i−2i−2i-2-222−2i−2i2i2i000000002i−2i−2i2i00000000000000000000000000000000
χ542-22-22-22-22-22-222-22-22-2-22i−2i−2i2i00000000-22-22-2-222−2i−2i2i2i22-2-22i2i−2i−2i000000002i−2i−2i2i00000000000000000000000000000000
χ552-22-22-22-22-22-222-22-22-2-2−2i2i2i−2i00000000-22-2222-2-2−2i−2i2i2i-2-2222i2i−2i−2i00000000−2i2i2i−2i00000000000000000000000000000000
χ562-22-22-22-22-22-222-22-22-2-2−2i2i2i−2i00000000-22-22-2-2222i2i−2i−2i22-2-2−2i−2i2i2i00000000−2i2i2i−2i00000000000000000000000000000000
χ572-22-22-22-2-12-22-2-11-11-1112i−2i2i−2i22-2-22i2i−2i−2i-11-1100000000000000002-22-22i−2i2i−2i−ii−ii-1-111−i−iii00000000-11−ii-11−ii00000000
χ582-22-22-22-2-12-22-2-11-11-1112i−2i2i−2i22-2-22i2i−2i−2i-11-110000000000000000-22-22−2i2i−2i2i−ii−ii-1-111−i−iii000000001-1i−i1-1i−i00000000
χ592-22-22-22-2-12-22-2-11-11-1112i−2i2i−2i-2-222−2i−2i2i2i-11-1100000000000000002-2-222i−2i−2i2i−ii−ii11-1-1ii−i−i00000000-11−ii1-1i−i00000000
χ602-22-22-22-2-12-22-2-11-11-1112i−2i2i−2i-2-222−2i−2i2i2i-11-110000000000000000-222-2−2i2i2i−2i−ii−ii11-1-1ii−i−i000000001-1i−i-11−ii00000000
χ612-22-22-22-2-12-22-2-11-11-111−2i2i−2i2i22-2-2−2i−2i2i2i-11-1100000000000000002-22-2−2i2i−2i2ii−ii−i-1-111ii−i−i00000000-11i−i-11i−i00000000
χ622-22-22-22-2-12-22-2-11-11-111−2i2i−2i2i22-2-2−2i−2i2i2i-11-110000000000000000-22-222i−2i2i−2ii−ii−i-1-111ii−i−i000000001-1−ii1-1−ii00000000
χ632-22-22-22-2-12-22-2-11-11-111−2i2i−2i2i-2-2222i2i−2i−2i-11-1100000000000000002-2-22−2i2i2i−2ii−ii−i11-1-1−i−iii00000000-11i−i1-1−ii00000000
χ642-22-22-22-2-12-22-2-11-11-111−2i2i−2i2i-2-2222i2i−2i−2i-11-110000000000000000-222-22i−2i−2i2ii−ii−i11-1-1−i−iii000000001-1−ii-11i−i00000000
χ652-2-22-2-222222-2-2-2-222-2-2200002i−2i−2i2i000022-2-200002-2-2200002-2-220000000000002i−2i−2i2i00000000−2i2i2i−2i0000000000000000
χ662-2-22-2-222222-2-2-2-222-2-2200002i−2i−2i2i000022-2-20000-222-20000-222-20000000000002i−2i−2i2i000000002i−2i−2i2i0000000000000000
χ672-2-22-2-222222-2-2-2-222-2-220000−2i2i2i−2i000022-2-200002-2-2200002-2-22000000000000−2i2i2i−2i000000002i−2i−2i2i0000000000000000
χ682-2-22-2-222222-2-2-2-222-2-220000−2i2i2i−2i000022-2-20000-222-20000-222-2000000000000−2i2i2i−2i00000000−2i2i2i−2i0000000000000000
χ692-2-22-2-2222-2-222-2-222-2-22000000002-2-22-2-22200002-2-220000-222-200000000000000002-2-222-2-2200000000000000000000
χ702-2-22-2-2222-2-222-2-222-2-22000000002-2-22-2-2220000-222-200002-2-2200000000000000002-2-22-222-200000000000000000000
χ712-2-22-2-2222-2-222-2-222-2-2200000000-222-2-2-22200002-2-220000-222-20000000000000000-222-2-222-200000000000000000000
χ722-2-22-2-2222-2-222-2-222-2-2200000000-222-2-2-2220000-222-200002-2-220000000000000000-222-22-2-2200000000000000000000
χ7344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4000000002222000000000000000000000000-2-22200000000000000000000000000000000
χ7444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44400000000222200000000000000000000000022-2-200000000000000000000000000000000
χ75444-4-4-4-4440000-44-4-44-440000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ76444-4-4-4-4440000-44-4-44-44000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ7744-444-4-4-44000044-44-4-4-400000000000000004-44-400000000000000000000000000000000000000000000000000000000
χ7844-444-4-4-44000044-44-4-4-40000000000000000-44-4400000000000000000000000000000000000000000000000000000000
χ7944-4-4-444-4-24-4-442-2-222-2200004i−4i4i−4i0000-222-20000000000000000000000000000−2i2i−2i2i0000000000000000000000000000
χ8044-4-4-444-4-24-4-442-2-222-220000−4i4i−4i4i0000-222-200000000000000000000000000002i−2i2i−2i0000000000000000000000000000
χ8144-4-4-444-4-2-444-42-2-222-22000000004i−4i4i−4i2-2-2200000000000000000000000000000000−2i2i−2i2i000000000000000000000000
χ8244-4-4-444-4-2-444-42-2-222-2200000000−4i4i−4i4i2-2-22000000000000000000000000000000002i−2i2i−2i000000000000000000000000
χ834-444-44-4-440000-4-4-4444-40000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ844-444-44-4-440000-4-4-4444-4000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ854-44-44-44-4-2-44-44-22-22-2224i−4i−4i4i000000002-22-2000000000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ864-44-44-44-4-2-44-44-22-22-222−4i4i4i−4i000000002-22-20000000000000000000000002i−2i−2i2i00000000000000000000000000000000
χ874-4-44-4-444-244-4-422-2-222-200004i−4i−4i4i0000-2-2220000000000000000000000000000−2i2i2i−2i0000000000000000000000000000
χ884-4-44-4-444-244-4-422-2-222-20000−4i4i4i−4i0000-2-22200000000000000000000000000002i−2i−2i2i0000000000000000000000000000
χ894-4-44-4-444-2-4-44422-2-222-2000000004-4-4422-2-200000000000000000000000000000000-222-2000000000000000000000000
χ904-4-44-4-444-2-4-44422-2-222-200000000-444-422-2-2000000000000000000000000000000002-2-22000000000000000000000000
χ914-4-4-444-44400004-4-4-4-44400000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ924-4-4-444-44400004-4-4-4-4440000000000000000-444-400000000000000000000000000000000000000000000000000000000
χ93888-8-8-8-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ9488-888-8-8-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000000000000000
χ958-888-88-8-8-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-888-88-40000-44444-4-40000000000000000000000000000000000000000000000000000000000000000000000000000

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