Finite Group Databasebeta

← Group #10711981

Character table — Group #10711981

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222244444444444444444444444444444444444444444488888888888888888888888824242424484848484848
order1222223666666622224444444444444412121212121212121212121212121212121212121212121222444466666666121212121212121212124444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-111-1-1
χ61111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111
χ71111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ911-1-11-11-1111-1-1-1-1-1111ii−i−iii−i−i11-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1i−ii−i11-1-111-1-11-1ii−i−iii−i−ii−ii−i1-11-1i−i
χ1011-1-11-11-1111-1-1-1-1-1111ii−i−iii−i−i11-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1i−ii−i11-1-111-1-11-1ii−i−iii−i−i−ii−ii-11-11−ii
χ1111-1-11-11-1111-1-1-1-1-1111ii−i−i−i−iii-1-111-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11i−i−ii11-1-1-1-1111-1ii−i−i−i−iiii−ii−i1-1-11−ii
χ1211-1-11-11-1111-1-1-1-1-1111ii−i−i−i−iii-1-111-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11i−i−ii11-1-1-1-1111-1ii−i−i−i−iii−ii−ii-111-1i−i
χ1311-1-11-11-1111-1-1-1-1-1111−i−iiiii−i−i-1-111-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11−iii−i11-1-1-1-1111-1−i−iiiii−i−ii−ii−i-111-1−ii
χ1411-1-11-11-1111-1-1-1-1-1111−i−iiiii−i−i-1-111-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11−iii−i11-1-1-1-1111-1−i−iiiii−i−i−ii−ii1-1-11i−i
χ1511-1-11-11-1111-1-1-1-1-1111−i−iii−i−iii11-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−ii−ii11-1-111-1-11-1−i−iii−i−iiii−ii−i-11-11i−i
χ1611-1-11-11-1111-1-1-1-1-1111−i−iii−i−iii11-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−ii−ii11-1-111-1-11-1−i−iii−i−iii−ii−ii1-11-1−ii
χ17222222222222222-22-2-2000022220000-20000000000000000222222220000-2-22-22-20000-2-20000-2-2-2-20000000000
χ18222222222222222-22-2-20000-2-2-2-20000-20000000000000000-2-2-2-2-2-2-2-20000222-22-20000-2-2000022220000000000
χ1922222222222222-22-22-2222200000000-200000000222222220000000000-2-200-22-220000-2-2-2-2-2-200000000000000
χ2022222222222222-22-22-2-2-2-2-200000000-200000000-2-2-2-2-2-2-2-200000000002200-22-220000-2-2222200000000000000
χ2122222222222222-2-2-2-220000000022222222222220000000000000000-2-20000-2-2-2-2-2-2-2-222000000000000000000
χ2222222222222222-2-2-2-2200000000-2-2-2-22-2-2-2-2-2-2-2-20000000000000000220000-2-2-2-2222222000000000000000000
χ23222222-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ24222222-1-1-1-1-1-1-1-1222222222-2-2-2-2-2-2-2-2211111111-1-1-1-1-1-1-1-111111111-2-222-2-2-1-1-1-11111-1-1-1-1-1-111110000000000
χ25222222-1-1-1-1-1-1-1-122222-2-2-2-22222-2-2-2-221111111111111111-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111-1-11111-1-1-1-10000000000
χ26222222-1-1-1-1-1-1-1-122222-2-2-2-2-2-2-2-222222-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000
χ27222222-1-1-1-1-1-1-1-12-22-2-2000022220000-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-1-1-1-1-1-1-10000-2-2-11-11−i3i3−i3i311−i3i3−i3i311110000000000
χ28222222-1-1-1-1-1-1-1-12-22-2-2000022220000-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-1-1-1-1-1-1-10000-2-2-11-11i3−i3i3−i311i3−i3i3−i311110000000000
χ29222222-1-1-1-1-1-1-1-12-22-2-20000-2-2-2-20000-2−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311111111000022-11-11−i3i3−i3i311i3−i3i3−i3-1-1-1-10000000000
χ30222222-1-1-1-1-1-1-1-12-22-2-20000-2-2-2-20000-2i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311111111000022-11-11i3−i3i3−i311−i3i3−i3i3-1-1-1-10000000000
χ31222222-1-1-1-1-1-1-1-1-22-22-2222200000000-2−i3−i3i3i3−i3−i3i3i3-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i300-2-2001-11-1i3−i3i3−i3111111−i3i3−i3i30000000000
χ32222222-1-1-1-1-1-1-1-1-22-22-2222200000000-2i3i3−i3−i3i3i3−i3−i3-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i300-2-2001-11-1−i3i3−i3i3111111i3−i3i3−i30000000000
χ33222222-1-1-1-1-1-1-1-1-22-22-2-2-2-2-200000000-2−i3−i3i3i3−i3−i3i3i311111111i3i3−i3−i3i3i3−i3−i30022001-11-1i3−i3i3−i311-1-1-1-1i3−i3i3−i30000000000
χ34222222-1-1-1-1-1-1-1-1-22-22-2-2-2-2-200000000-2i3i3−i3−i3i3i3−i3−i311111111−i3−i3i3i3−i3−i3i3i30022001-11-1−i3i3−i3i311-1-1-1-1−i3i3−i3i30000000000
χ35222222-1-1-1-1-1-1-1-1-2-2-2-220000000022222-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-2-2000011111111-1-1i3−i3i3−i3i3−i3i3−i30000000000
χ36222222-1-1-1-1-1-1-1-1-2-2-2-220000000022222-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-2-2000011111111-1-1−i3i3−i3i3−i3i3−i3i30000000000
χ37222222-1-1-1-1-1-1-1-1-2-2-2-2200000000-2-2-2-2211111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32200001111-1-1-1-1-1-1i3−i3i3−i3−i3i3−i3i30000000000
χ38222222-1-1-1-1-1-1-1-1-2-2-2-2200000000-2-2-2-2211111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i32200001111-1-1-1-1-1-1−i3i3−i3i3i3−i3i3−i30000000000
χ3922-2-22-22-2222-2-2-222-2-220000000022-2-2-22222-2-2-2-20000000000000000-220000-2-222-2-2222-2000000000000000000
χ4022-2-22-22-2222-2-2-222-2-2200000000-2-222-2-2-2-2-2222200000000000000002-20000-2-22222-2-22-2000000000000000000
χ4122-2-22-22-2222-2-2-22-2-22-22i2i−2i−2i000000002000000002i2i2i2i−2i−2i−2i−2i0000000000−2i2i00-222-20000-22−2i−2i2i2i00000000000000
χ4222-2-22-22-2222-2-2-22-2-22-2−2i−2i2i2i00000000200000000−2i−2i−2i−2i2i2i2i2i00000000002i−2i00-222-20000-222i2i−2i−2i00000000000000
χ4322-2-22-22-2222-2-2-2-222-2-200002i2i−2i−2i0000200000000000000002i2i2i2i−2i−2i−2i−2i0000−2i2i2-2-220000-220000−2i−2i2i2i0000000000
χ4422-2-22-22-2222-2-2-2-222-2-20000−2i−2i2i2i000020000000000000000−2i−2i−2i−2i2i2i2i2i00002i−2i2-2-220000-2200002i2i−2i−2i0000000000
χ4522-2-22-2-11-1-1-111122-2-220000000022-2-2-2-1-1-1-1111133−3−3−3−33333−3−3−3−333-22000011-1-111-1-1-11−333−3−333−30000000000
χ4622-2-22-2-11-1-1-111122-2-220000000022-2-2-2-1-1-1-11111−3−33333−3−3−3−33333−3−3-22000011-1-111-1-1-113−3−333−3−330000000000
χ4722-2-22-2-11-1-1-111122-2-2200000000-2-222-21111-1-1-1-133−3−3−3−333−3−33333−3−32-2000011-1-1-1-111-11−333−33−3−330000000000
χ4822-2-22-2-11-1-1-111122-2-2200000000-2-222-21111-1-1-1-1−3−33333−3−333−3−3−3−3332-2000011-1-1-1-111-113−3−33−333−30000000000
χ4922-2-22-2-11-1-1-11112-2-22-22i2i−2i−2i000000002−i3−i3i3i3i3i3−i3−i3−i−i−i−iiiii33−3−3−3−33300−2i2i001-1-11i3−i3−i3i31-1ii−i−i3−3−330000000000
χ5022-2-22-2-11-1-1-11112-2-22-22i2i−2i−2i000000002i3i3−i3−i3−i3−i3i3i3−i−i−i−iiiii−3−33333−3−300−2i2i001-1-11−i3i3i3−i31-1ii−i−i−333−30000000000
χ5122-2-22-2-11-1-1-11112-2-22-2−2i−2i2i2i000000002−i3−i3i3i3i3i3−i3−i3iiii−i−i−i−i−3−33333−3−3002i−2i001-1-11i3−i3−i3i31-1−i−iii−333−30000000000
χ5222-2-22-2-11-1-1-11112-2-22-2−2i−2i2i2i000000002i3i3−i3−i3−i3−i3i3i3iiii−i−i−i−i33−3−3−3−333002i−2i001-1-11−i3i3i3−i31-1−i−iii3−3−330000000000
χ5322-2-22-2-11-1-1-1111-222-2-200002i2i−2i−2i00002−i3−i3i3i3i3i3−i3−i333−3−3−3−333−i−i−i−iiiii0000−2i2i-111-1−i3i3i3−i31-13−3−33ii−i−i0000000000
χ5422-2-22-2-11-1-1-1111-222-2-200002i2i−2i−2i00002i3i3−i3−i3−i3−i3i3i3−3−33333−3−3−i−i−i−iiiii0000−2i2i-111-1i3−i3−i3i31-1−333−3ii−i−i0000000000
χ5522-2-22-2-11-1-1-1111-222-2-20000−2i−2i2i2i00002−i3−i3i3i3i3i3−i3−i3−3−33333−3−3iiii−i−i−i−i00002i−2i-111-1−i3i3i3−i31-1−333−3−i−iii0000000000
χ5622-2-22-2-11-1-1-1111-222-2-20000−2i−2i2i2i00002i3i3−i3−i3−i3−i3i3i333−3−3−3−333iiii−i−i−i−i00002i−2i-111-1i3−i3−i3i31-13−3−33−i−iii0000000000
χ5722-2-22-2-11-1-1-1111-2-22222i2i−2i−2i2i2i−2i−2i22-2-2-2-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii2-22i−2i2i−2i-1-111-1-111-11−i−iii−i−iii0000000000
χ5822-2-22-2-11-1-1-1111-2-22222i2i−2i−2i−2i−2i2i2i-2-222-21111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-222i−2i−2i2i-1-11111-1-1-11−i−iiiii−i−i0000000000
χ5922-2-22-2-11-1-1-1111-2-2222−2i−2i2i2i2i2i−2i−2i-2-222-21111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-22−2i2i2i−2i-1-11111-1-1-11ii−i−i−i−iii0000000000
χ6022-2-22-2-11-1-1-1111-2-2222−2i−2i2i2i−2i−2i2i2i22-2-2-2-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i2-2−2i2i−2i2i-1-111-1-111-11ii−i−iii−i−i0000000000
χ614444-4-4444-4-4-4-4400000000000000000000000000000000000000000000000000000000000000000022-2-2000000
χ624444-4-4444-4-4-4-44000000000000000000000000000000000000000000000000000000000000000000-2-222000000
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χ684-44-40044-40000-400000−2i2i−2i2i−2i2i−2i2i2-22-202-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ694-44-400-2-22−2i32i3−2i32i32000002i−2i2i−2i2i−2i2i−2i2-22-20−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000000000000000
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χ734-44-400-2-222i3−2i32i3−2i32000002i−2i2i−2i2i−2i2i−2i2-22-20−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000000000000000
χ744-44-400-2-222i3−2i32i3−2i32000002i−2i2i−2i−2i2i−2i2i-22-2201−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000000000000000
χ754-44-400-2-222i3−2i32i3−2i3200000−2i2i−2i2i2i−2i2i−2i-22-2201−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000000000000000
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χ774-4-44004-4-400004000002-2-222-2-222-2-2202-22-2-22-222-22-2-22-222-22-2-22-220000000000000000000000000000000000
χ784-4-44004-4-400004000002-2-22-222-2-222-20-22-222-22-22-22-2-22-22-22-222-22-20000000000000000000000000000000000
χ794-4-44004-4-40000400000-222-22-2-22-222-20-22-222-22-2-22-222-22-22-22-2-22-220000000000000000000000000000000000
χ804-4-44004-4-40000400000-222-2-222-22-2-2202-22-2-22-22-22-222-22-2-22-222-22-20000000000000000000000000000000000
χ814-4-4400-222−2i32i32i3−2i3-2000002-2-222-2-222-2-220−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000000000000000
χ824-4-4400-222−2i32i32i3−2i3-2000002-2-22-222-2-222-201+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000000000000000
χ834-4-4400-222−2i32i32i3−2i3-200000-222-22-2-22-222-201+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000000000000000
χ844-4-4400-222−2i32i32i3−2i3-200000-222-2-222-22-2-220−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000000000000000
χ854-4-4400-2222i3−2i3−2i32i3-2000002-2-222-2-222-2-220−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000000000000000
χ864-4-4400-2222i3−2i3−2i32i3-2000002-2-22-222-2-222-201−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000000000000000
χ874-4-4400-2222i3−2i3−2i32i3-200000-222-22-2-22-222-201−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000000000000000
χ884-4-4400-2222i3−2i3−2i32i3-200000-222-2-222-22-2-220−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000000000000000
χ898888-8-8-4-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-88-44-444-4-440000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.