Finite Group Databasebeta

← Group #10690313

Character table — Group #10690313

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222222222444444448888888888888888888888888888888888888824242424242424242424242424242424
order1222222222223666666666666666444444444444444444121212121212121212121212121212121212121212121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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χ1011-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111-1ii−i−i1-1i−i11-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1-11-11−ii−ii-1-111−i−iii
χ1111-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111-1ii−i−i1-1i−i-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1-1-111111-11-1i−ii−i-1-111−i−iii
χ1211-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111-1ii−i−i1-1i−i-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1-1-11111-11-11−ii−ii11-1-1ii−i−i
χ1311-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111-1−i−iii1-1−ii11-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-11-11-1−ii−ii11-1-1−i−iii
χ1411-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111-1−i−iii1-1−ii11-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1-11-11i−ii−i-1-111ii−i−i
χ1511-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111-1−i−iii1-1−ii-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1-1-111111-11-1−ii−ii-1-111ii−i−i
χ1611-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111-1−i−iii1-1−ii-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1-1-11111-11-11i−ii−i11-1-1−i−iii
χ172222222222222222222222222222-2-22222-2-2-2-20000000022-2-222-2-200000000-2-2-2-2000000000000000000000000
χ182222222222222222222222222222-2-2-2-2-2-2-2-22200000000-2-222-2-22200000000-2-2-2-2000000000000000000000000
χ19222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1111111110000000000000000
χ21222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-22222-2-2-2-21111111111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000
χ23222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-200000000-1-111-1-111−i3−i3i3i3−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i30000000000000000
χ24222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-200000000-1-111-1-111i3i3−i3−i3i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i30000000000000000
χ25222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2220000000011-1-111-1-1−i3−i3i3i3−i3−i3i3i31111i3i3−i3−i3i3i3−i3−i30000000000000000
χ26222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2220000000011-1-111-1-1i3i3−i3−i3i3i3−i3−i31111−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222222-2-2-2-2222-2-2-2-222-2-222-2-222-20000-22000000000000000000000000002-22-200000000000022-2-200000000
χ2822222222-2-2-2-2222-2-2-2-222-2-222-2-222-20000-22000000000000000000000000002-22-2000000000000-2-22200000000
χ2922222222-2-2-2-2222-2-2-2-222-2-222-2-22-2200002-200000000000000000000000000-22-220000000022-2-2000000000000
χ3022222222-2-2-2-2222-2-2-2-222-2-222-2-22-2200002-200000000000000000000000000-22-2200000000-2-222000000000000
χ3122-2-222-2-222-2-22222222-2-2-2-2-2-2-2-22-222i2i−2i−2i-22−2i2i000000002i2i−2i−2i−2i−2i2i2i00000000-2-222000000000000000000000000
χ3222-2-222-2-222-2-22222222-2-2-2-2-2-2-2-22-22−2i−2i2i2i-222i−2i00000000−2i−2i2i2i2i2i−2i−2i00000000-2-222000000000000000000000000
χ3322-2-222-2-222-2-2-1-1-1-1-1-1-111111111-12-22i2i−2i−2i2-22i−2i22-2-22i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-111110000000000000000
χ3422-2-222-2-222-2-2-1-1-1-1-1-1-111111111-12-22i2i−2i−2i2-22i−2i-2-222−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i-1-1111111-1-1-1-10000000000000000
χ3522-2-222-2-222-2-2-1-1-1-1-1-1-111111111-12-2−2i−2i2i2i2-2−2i2i22-2-2−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-111110000000000000000
χ3622-2-222-2-222-2-2-1-1-1-1-1-1-111111111-12-2−2i−2i2i2i2-2−2i2i-2-2222i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii-1-1111111-1-1-1-10000000000000000
χ3722-2-222-2-222-2-2-1-1-1-1-1-1-111111111-1-222i2i−2i−2i-22−2i2i00000000−i−iiiii−i−i33−3−3−3−33311-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3822-2-222-2-222-2-2-1-1-1-1-1-1-111111111-1-222i2i−2i−2i-22−2i2i00000000−i−iiiii−i−i−3−33333−3−311-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3922-2-222-2-222-2-2-1-1-1-1-1-1-111111111-1-22−2i−2i2i2i-222i−2i00000000ii−i−i−i−iii33−3−3−3−33311-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ4022-2-222-2-222-2-2-1-1-1-1-1-1-111111111-1-22−2i−2i2i2i-222i−2i00000000ii−i−i−i−iii−3−33333−3−311-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ4122-2-222-2-2-2-222222-2-2-2-2-2-222-2-2222220000-2-2000000000000000000000000002-2-220000000000002i−2i−2i2i00000000
χ4222-2-222-2-2-2-222222-2-2-2-2-2-222-2-2222220000-2-2000000000000000000000000002-2-22000000000000−2i2i2i−2i00000000
χ4322-2-222-2-2-2-222222-2-2-2-2-2-222-2-2222-2-200002200000000000000000000000000-222-2000000002-2-22000000000000
χ4422-2-222-2-2-2-222222-2-2-2-2-2-222-2-2222-2-200002200000000000000000000000000-222-200000000-222-2000000000000
χ452-2222-2-2-22-2-2222-222-2-22-2-2-22-222-2002i−2i2i−2i0000000000002i−2i002i−2i000000000000000000000000000000−i2i2−i2i22−22−2
χ462-2222-2-2-22-2-2222-222-2-22-2-2-22-222-2002i−2i2i−2i0000000000002i−2i002i−2i000000000000000000000000000000i2−i2i2−i2−22−22
χ472-2222-2-2-22-2-2222-222-2-22-2-2-22-222-200−2i2i−2i2i000000000000−2i2i00−2i2i000000000000000000000000000000−i2i2−i2i2−22−22
χ482-2222-2-2-22-2-2222-222-2-22-2-2-22-222-200−2i2i−2i2i000000000000−2i2i00−2i2i000000000000000000000000000000i2−i2i2−i22−22−2
χ492-2-2-22-2222-22-222-222-2-2-2222-22-2-2-2002-2-220000000000002-200-22000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ502-2-2-22-2222-22-222-222-2-2-2222-22-2-2-2002-2-220000000000002-200-22000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ512-2-2-22-2222-22-222-222-2-2-2222-22-2-2-200-222-2000000000000-22002-2000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ522-2-2-22-2222-22-222-222-2-2-2222-22-2-2-200-222-2000000000000-22002-2000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ5344444444-4-4-4-4-2-2-22222-2-222-2-222-24-40000-4400000000000000000000000000-22-22000000000000000000000000
χ5444444444-4-4-4-4-2-2-22222-2-222-2-222-2-4400004-4000000000000000000000000002-22-2000000000000000000000000
χ55444-4-4-44-400004-4400004400-4-400-4000000000000002-22-2000000002-22-22-22-20000000000000000000000000000
χ56444-4-4-44-400004-4400004400-4-400-400000000000000-22-2200000000-22-22-22-220000000000000000000000000000
χ57444-4-4-44-40000-22-2−2i32i3−2i32i3-2-2−2i32i322−2i32i32000000000000002-22-200000000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000000000000000
χ58444-4-4-44-40000-22-2−2i32i3−2i32i3-2-2−2i32i322−2i32i3200000000000000-22-22000000001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000000000000000
χ59444-4-4-44-40000-22-22i3−2i32i3−2i3-2-22i3−2i3222i3−2i32000000000000002-22-200000000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000000000000000
χ60444-4-4-44-40000-22-22i3−2i32i3−2i3-2-22i3−2i3222i3−2i3200000000000000-22-22000000001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000000000000000
χ6144-44-4-4-4400004-440000-4-4004400-4000000000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ6244-44-4-4-4400004-440000-4-4004400-400000000000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ6344-44-4-4-440000-22-2−2i32i3−2i32i3222i3−2i3-2-22i3−2i32000000000000002i−2i−2i2i000000002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ6444-44-4-4-440000-22-2−2i32i3−2i32i3222i3−2i3-2-22i3−2i3200000000000000−2i2i2i−2i00000000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ6544-44-4-4-440000-22-22i3−2i32i3−2i322−2i32i3-2-2−2i32i32000000000000002i−2i−2i2i000000002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ6644-44-4-4-440000-22-22i3−2i32i3−2i322−2i32i3-2-2−2i32i3200000000000000−2i2i2i−2i00000000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ6744-4-444-4-4-4-444-2-2-2222222-2-222-2-2-2440000-4-400000000000000000000000000-222-2000000000000000000000000
χ6844-4-444-4-4-4-444-2-2-2222222-2-222-2-2-2-4-4000044000000000000000000000000002-2-22000000000000000000000000
χ694-4444-4-4-44-4-44-2-22-2-222-2222-22-2-22004i−4i4i−4i000000000000−2i2i00−2i2i00000000000000000000000000000000000000
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χ714-4444-4-4-4-444-444-4-4-4444-4444-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ724-4444-4-4-4-444-4-2-2222-2-2-22-2-2-2222200000000000000000000−2i32i300−2i32i3000000000000000000000000000000000000
χ734-4444-4-4-4-444-4-2-2222-2-2-22-2-2-22222000000000000000000002i3−2i3002i3−2i3000000000000000000000000000000000000
χ744-44-4-44-4400004-4-400004-400-4400400000000002-22-20000000000000000000000002-22-22-22-20000000000000000
χ754-44-4-44-4400004-4-400004-400-440040000000000-22-22000000000000000000000000-22-22-22-220000000000000000
χ764-44-4-44-440000-222−2i32i32i3−2i3-222i3−2i32-2−2i32i3-200000000002-22-2000000000000000000000000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000
χ774-44-4-44-440000-222−2i32i32i3−2i3-222i3−2i32-2−2i32i3-20000000000-22-220000000000000000000000001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000
χ784-44-4-44-440000-2222i3−2i3−2i32i3-22−2i32i32-22i3−2i3-200000000002-22-2000000000000000000000000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000
χ794-44-4-44-440000-2222i3−2i3−2i32i3-22−2i32i32-22i3−2i3-20000000000-22-220000000000000000000000001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000
χ804-4-44-444-400004-4-40000-44004-400400000000002-2-220000000000000000000000002-22-2-22-220000000000000000
χ814-4-44-444-400004-4-40000-44004-40040000000000-222-2000000000000000000000000-22-222-22-20000000000000000
χ824-4-44-444-40000-222−2i32i32i3−2i32-2−2i32i3-222i3−2i3-200000000002-2-22000000000000000000000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000
χ834-4-44-444-40000-222−2i32i32i3−2i32-2−2i32i3-222i3−2i3-20000000000-222-20000000000000000000000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000
χ844-4-44-444-40000-2222i3−2i3−2i32i32-22i3−2i3-22−2i32i3-200000000002-2-22000000000000000000000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000
χ854-4-44-444-40000-2222i3−2i3−2i32i32-22i3−2i3-22−2i32i3-20000000000-222-20000000000000000000000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000
χ864-4-4-44-4444-44-4-2-22-2-2222-2-2-22-2222004-4-44000000000000-22002-200000000000000000000000000000000000000
χ874-4-4-44-4444-44-4-2-22-2-2222-2-2-22-222200-444-40000000000002-200-2200000000000000000000000000000000000000
χ884-4-4-44-444-44-4444-4-4-444-44-4-4-4444-400000000000000000000000000000000000000000000000000000000000000
χ894-4-4-44-444-44-44-2-2222-2-22-2222-2-2-220000000000000000000023−2300−2323000000000000000000000000000000000000
χ904-4-4-44-444-44-44-2-2222-2-22-2222-2-2-2200000000000000000000−23230023−23000000000000000000000000000000000000

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