Finite Group Databasebeta

← Group #10713296

Character table — Group #10713296

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12222234444666666688888888444488881212121212121212121212122424242424242424242424242424242444441212121212121212444488881616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911-1-1-111-111-1-1-1111-1-1-1-111-1-11111-1-11-11-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011-1-1-111-111-1-1-1111-1-1-1-111-1-11111-1-11-11-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1111-1-1-111-111-1-1-1111-1-1-1-111-1-11111-1-11-11-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ1211-1-1-111-111-1-1-1111-1-1-1-111-1-11111-1-11-11-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1311-1-1-111-111-1-1-1111-1-1-1-1-1-11111-1-1111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ1411-1-1-111-111-1-1-1111-1-1-1-1-1-11111-1-1111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ1511-1-1-111-111-1-1-1111-1-1-1-1-1-11111-1-1111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ1611-1-1-111-111-1-1-1111-1-1-1-1-1-11111-1-1111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222222222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ19222222-12222-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ20222222-12222-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ21222222-12222-1-1-1-1-1-1-122-2-2-2-222-2-2-2-222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ22222222-12222-1-1-1-1-1-1-122-2-2-2-222-2-2-2-222-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ23222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-2-222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3−i3i3−i3i30000000000000000
χ24222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-2-222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3i3−i3i3−i30000000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ272222-2-2222-2-2-2-22-2-222220000220000-2-2002-2000000002-222-2-222-2-2000000000000000000002-22-2000000000000
χ282222-2-2222-2-2-2-22-2-222220000220000-2-2002-2000000002-222-2-222-2-200000000000000000000-22-22000000000000
χ292222-2-2222-2-2-2-22-2-222-2-20000-2-2000022002-2000000002-2-2-222-2-2220000000000000000000000002i−2i2i−2i00000000
χ302222-2-2222-2-2-2-22-2-222-2-20000-2-2000022002-2000000002-2-2-222-2-222000000000000000000000000−2i2i−2i2i00000000
χ312222-2-22-2-222-2-22-2-22200222200000000-2-2-2200000000-220000000022-2-222-2-2000000000000000000002−22−22−22−2
χ322222-2-22-2-222-2-22-2-22200222200000000-2-2-2200000000-220000000022-2-222-2-200000000000000000000−22−22−22−22
χ332222-2-22-2-222-2-22-2-22200-2-2-2-20000000022-2200000000-2200000000-2-222-2-222000000000000000000002−22−2−22−22
χ342222-2-22-2-222-2-22-2-22200-2-2-2-20000000022-2200000000-2200000000-2-222-2-22200000000000000000000−22−222−22−2
χ3522-2-22-222-22-2222-2-2-2-20022-2-200000000-222-200000000-220000000022-2-2-2-222000000000000000000002−2−222−2−22
χ3622-2-22-222-22-2222-2-2-2-20022-2-200000000-222-200000000-220000000022-2-2-2-22200000000000000000000−222−2−222−2
χ3722-2-22-222-22-2222-2-2-2-200-2-222000000002-22-200000000-2200000000-2-22222-2-2000000000000000000002−2−22−222−2
χ3822-2-22-222-22-2222-2-2-2-200-2-222000000002-22-200000000-2200000000-2-22222-2-200000000000000000000−222−22−2−22
χ3922-2-22-22-22-22222-2-2-2-2220000-2-200002-200-22000000002-2-2-22222-2-20000000000000000000000002-2-2200000000
χ4022-2-22-22-22-22222-2-2-2-2220000-2-200002-200-22000000002-2-2-22222-2-2000000000000000000000000-222-200000000
χ4122-2-22-22-22-22222-2-2-2-2-2-20000220000-2200-22000000002-222-2-2-2-222000000000000000000002i−2i−2i2i000000000000
χ4222-2-22-22-22-22222-2-2-2-2-2-20000220000-2200-22000000002-222-2-2-2-22200000000000000000000−2i2i2i−2i000000000000
χ4322-2-2-222-222-2-2-2222-2-22222-2-2-2-2-2-222-222-2-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ4422-2-2-222-222-2-2-2222-2-222-2-222-2-222-2-2-22-22-2-22222-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ4522-2-2-22-1-222-211-1-1-1112222-2-2-2-2-2-222-222-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−333−3−330000000000000000
χ4622-2-2-22-1-222-211-1-1-1112222-2-2-2-2-2-222-222-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−3−333−30000000000000000
χ4722-2-2-22-1-222-211-1-1-11122-2-222-2-222-2-2-22-2211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-100003−3−33−333−30000000000000000
χ4822-2-2-22-1-222-211-1-1-11122-2-222-2-222-2-2-22-2211-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-10000−333−33−3−330000000000000000
χ4922-2-2-22-1-222-211-1-1-111-2-222-2-22222-2-22-22-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111112i−2i2i−2i−i−iii−i−iii0000000000000000
χ5022-2-2-22-1-222-211-1-1-111-2-222-2-22222-2-22-22-211-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ5122-2-2-22-1-222-211-1-1-111-2-2-2-22222-2-2222-2-22111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-12i−2i−2i2i−i−iiiii−i−i0000000000000000
χ5222-2-2-22-1-222-211-1-1-111-2-2-2-22222-2-2222-2-22111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−2i2i2i−2iii−i−i−i−iii0000000000000000
χ534444444-4-4-4-444444440000000000000000-4-400000000-4-400000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2-2-2000000000000000022−2i3−2i32i32i3−2i3−2i32i32i32200000000000000000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-2-2-2-2-20000000000000000222i32i3−2i3−2i32i32i3−2i3−2i32200000000000000000000000000000000000000000000
χ564444-4-4-244-4-422-222-2-2440000440000-4-400-2200000000-22-2-222-2-222000000000000000000000000000000000000
χ574444-4-4-244-4-422-222-2-2-4-40000-4-400004400-2200000000-2222-2-222-2-2000000000000000000000000000000000000
χ584444-4-4-2-4-44422-222-2-200444400000000-4-42-2000000002-200000000-2-222-2-2220000000000000000000000000000
χ594444-4-4-2-4-44422-222-2-200-4-4-4-400000000442-2000000002-20000000022-2-222-2-20000000000000000000000000000
χ6044-4-44-4-24-44-4-2-2-222220044-4-400000000-44-22000000002-200000000-2-22222-2-20000000000000000000000000000
χ6144-4-44-4-24-44-4-2-2-2222200-4-444000000004-4-22000000002-20000000022-2-2-2-2220000000000000000000000000000
χ6244-4-44-4-2-44-44-2-2-22222440000-4-400004-4002-200000000-2222-2-2-2-222000000000000000000000000000000000000
χ6344-4-44-4-2-44-44-2-2-22222-4-40000440000-44002-200000000-22-2-22222-2-2000000000000000000000000000000000000
χ6444-4-4-4444-4-44-4-4444-4-400000000000000004400000000-4-400000000000000000000000000000000000000000000
χ6544-4-4-44-24-4-4422-2-2-2220000000000000000-2-2−2i3−2i32i32i32i32i3−2i3−2i32200000000000000000000000000000000000000000000
χ6644-4-4-44-24-4-4422-2-2-2220000000000000000-2-22i32i3−2i3−2i3−2i3−2i32i32i32200000000000000000000000000000000000000000000
χ674-44-4004000000-4004-422−22−2i22i2−2i22i222−222i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0022−220022−2200−2i22i200−2i22i2000000000000000000000000000000
χ684-44-4004000000-4004-422−222i2−2i22i2−2i222−22−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0022−220022−22002i2−2i2002i2−2i2000000000000000000000000000000
χ694-44-4004000000-4004-4−2222−2i22i2−2i22i2−2222−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i00−222200−222200−2i22i200−2i22i2000000000000000000000000000000
χ704-44-4004000000-4004-4−22222i2−2i22i2−2i2−22222i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i00−222200−2222002i2−2i2002i2−2i2000000000000000000000000000000
χ714-44-400-20000−2i32i32−2i32i3-2222−22−2i22i2−2i22i222−222i−2i2i−2i0000002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ2200−22i6−i6−22i6−i6i2−i26−6i2−i26−60000000000000000000000000000
χ724-44-400-20000−2i32i32−2i32i3-2222−222i2−2i22i2−2i222−22−2i2i−2i2i000000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ2200−22i6−i6−22i6−i6−i2i2−66−i2i2−660000000000000000000000000000
χ734-44-400-20000−2i32i32−2i32i3-22−2222−2i22i2−2i22i2−2222−2i2i−2i2i000000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22002−2−i6i62−2−i6i6i2−i26−6i2−i26−60000000000000000000000000000
χ744-44-400-20000−2i32i32−2i32i3-22−22222i2−2i22i2−2i2−22222i−2i2i−2i0000002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ22002−2−i6i62−2−i6i6−i2i2−66−i2i2−660000000000000000000000000000
χ754-44-400-200002i3−2i322i3−2i3-2222−22−2i22i2−2i22i222−222i−2i2i−2i0000002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ1400−22−i6i6−22−i6i6i2−i2−66i2−i2−660000000000000000000000000000
χ764-44-400-200002i3−2i322i3−2i3-2222−222i2−2i22i2−2i222−22−2i2i−2i2i000000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ1400−22−i6i6−22−i6i6−i2i26−6−i2i26−60000000000000000000000000000
χ774-44-400-200002i3−2i322i3−2i3-22−2222−2i22i2−2i22i2−2222−2i2i−2i2i000000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14002−2i6−i62−2i6−i6i2−i2−66i2−i2−660000000000000000000000000000
χ784-44-400-200002i3−2i322i3−2i3-22−22222i2−2i22i2−2i2−22222i−2i2i−2i0000002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ14002−2i6−i62−2i6−i6−i2i26−6−i2i26−60000000000000000000000000000
χ794-4-44004000000-400-4422−22−2i22i22i2−2i2−2222−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i00−22220022−2200−2i22i2002i2−2i2000000000000000000000000000000
χ804-4-44004000000-400-4422−222i2−2i2−2i22i2−22222i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i00−22220022−22002i2−2i200−2i22i2000000000000000000000000000000
χ814-4-44004000000-400-44−2222−2i22i22i2−2i222−222i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i0022−2200−222200−2i22i2002i2−2i2000000000000000000000000000000
χ824-4-44004000000-400-44−22222i2−2i2−2i22i222−22−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i0022−2200−2222002i2−2i200−2i22i2000000000000000000000000000000
χ834-4-4400-20000−2i32i322i3−2i32-222−22−2i22i22i2−2i2−2222−2i2i2i−2i000000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ14002−2i6−i6−22−i6i6i2−i2−66−i2i26−60000000000000000000000000000
χ844-4-4400-20000−2i32i322i3−2i32-222−222i2−2i2−2i22i2−22222i−2i−2i2i0000002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ14002−2i6−i6−22−i6i6−i2i26−6i2−i2−660000000000000000000000000000
χ854-4-4400-20000−2i32i322i3−2i32-2−2222−2i22i22i2−2i222−222i−2i−2i2i0000002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ1400−22−i6i62−2i6−i6i2−i2−66−i2i26−60000000000000000000000000000
χ864-4-4400-20000−2i32i322i3−2i32-2−22222i2−2i2−2i22i222−22−2i2i2i−2i000000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ1400−22−i6i62−2i6−i6−i2i26−6i2−i2−660000000000000000000000000000
χ874-4-4400-200002i3−2i32−2i32i32-222−22−2i22i22i2−2i2−2222−2i2i2i−2i000000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ22002−2−i6i6−22i6−i6i2−i26−6−i2i2−660000000000000000000000000000
χ884-4-4400-200002i3−2i32−2i32i32-222−222i2−2i2−2i22i2−22222i−2i−2i2i0000002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ22002−2−i6i6−22i6−i6−i2i2−66i2−i26−60000000000000000000000000000
χ894-4-4400-200002i3−2i32−2i32i32-2−2222−2i22i22i2−2i222−222i−2i−2i2i0000002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ2200−22i6−i62−2−i6i6i2−i26−6−i2i2−660000000000000000000000000000
χ904-4-4400-200002i3−2i32−2i32i32-2−22222i2−2i2−2i22i222−22−2i2i2i−2i000000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ2200−22i6−i62−2−i6i6−i2i2−66i2−i26−60000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.