Finite Group Databasebeta

← Group #10695579

Character table — Group #10695579

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order122222223446666666244466661212121222224444666666661212121212121212121244121212124444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1
χ6111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ9222222222-2-222222222-2-2-22222-2-2-2-22200-2-20022220000-2-2-2-2-2-200000000000000000000
χ10222222222-2-222222222-2-2-22222-2-2-2-2-2-2002200-2-2-2-200002222-2-200000000000000000000
χ1122222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ1222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-1-1-11111-2-211110000000000
χ1322222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-1-1-1-2-211110000000000
χ1422222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111-1-1111122-1-1-1-10000000000
χ1522222222-1-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-111112200-2-200-1-1-1-1−i3−i3i3i3111111−i3−i3i3i300−i3−i3i3i30000000000
χ1622222222-1-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-111112200-2-200-1-1-1-1i3i3−i3−i3111111i3i3−i3−i300i3i3−i3−i30000000000
χ1722222222-1-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-11111-2-20022001111−i3−i3i3i3-1-1-1-111−i3−i3i3i300i3i3−i3−i30000000000
χ1822222222-1-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-11111-2-20022001111i3i3−i3−i3-1-1-1-111i3i3−i3−i300−i3−i3i3i30000000000
χ19222222-2-22222222222-22-2-2-2-2-2-2222200000000000000000000-2-200002-22-22-20000000000
χ20222222-2-22222222222-22-2-2-2-2-2-2222200000000000000000000-2-20000-22-22-220000000000
χ21222222-2-22-2-22222222-2-222-2-2-2-2-2-2-2-2002200-2-200002222000022-2-2-2-20000000000000000
χ22222222-2-22-2-22222222-2-222-2-2-2-2-2-2-2-200-2-200220000-2-2-2-200002222220000000000000000
χ23222222-2-2-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311i3i3−i3−i32-2-11-110000000000
χ24222222-2-2-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i311−i3−i3i3i3-221-11-10000000000
χ25222222-2-2-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i311i3i3−i3−i3-221-11-10000000000
χ26222222-2-2-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311−i3−i3i3i32-2-11-110000000000
χ27222222-2-2-1-2-2-1-1-1-1-1-1-1-2-22211111111002200-2-2−i3−i3i3i3-1-1-1-1i3i3−i3−i3-1-1111100−i3i3i3−i30000000000
χ28222222-2-2-1-2-2-1-1-1-1-1-1-1-2-22211111111002200-2-2i3i3−i3−i3-1-1-1-1−i3−i3i3i3-1-1111100i3−i3−i3i30000000000
χ29222222-2-2-1-2-2-1-1-1-1-1-1-1-2-2221111111100-2-20022−i3−i3i3i31111i3i3−i3−i3-1-1-1-1-1-100i3−i3−i3i30000000000
χ30222222-2-2-1-2-2-1-1-1-1-1-1-1-2-2221111111100-2-20022i3i3−i3−i31111−i3−i3i3i3-1-1-1-1-1-100−i3i3i3−i30000000000
χ312222-2-2222222-2-2-2-222-2-22-222-2-222-2-2000000000000000000002-2000000000022-2-2000000
χ322222-2-2222222-2-2-2-222-2-22-222-2-222-2-2000000000000000000002-20000000000-2-222000000
χ332222-2-2222-2-22-2-2-2-222-22-2222-2-2-2-22200000000000000000000-22000000000000002-20000
χ342222-2-2222-2-22-2-2-2-222-22-2222-2-2-2-22200000000000000000000-2200000000000000-220000
χ352222-2-2-2-22222-2-2-2-2222-2-22-2-22222-2-200000000000000000000-220000000000000000002-2
χ362222-2-2-2-22222-2-2-2-2222-2-22-2-22222-2-200000000000000000000-22000000000000000000-22
χ372222-2-2-2-22-2-22-2-2-2-222222-2-2-222-2-222000000000000000000002-200000000000000002i−2i00
χ382222-2-2-2-22-2-22-2-2-2-222222-2-2-222-2-222000000000000000000002-20000000000000000−2i2i00
χ394444-4-444-244-22222-2-2-4-44-4-2-222-2-22200000000000000000000-2200000000000000000000
χ404444-4-444-2-4-4-22222-2-2-44-44-2-22222-2-2000000000000000000002-200000000000000000000
χ414444-4-4-4-4-244-22222-2-24-4-4422-2-2-2-222000000000000000000002-200000000000000000000
χ424444-4-4-4-4-2-4-4-22222-2-2444-422-2-222-2-200000000000000000000-2200000000000000000000
χ4344-4-44-400400-444-4-44-4000000000000000000000000000000000000000000002i−2i2i−2i000000
χ4444-4-44-400400-444-4-44-400000000000000000000000000000000000000000000−2i2i−2i2i000000
χ4544-4-4-4400400-4-4-4444-4000000000000000000000000000000000000000000002i−2i−2i2i000000
χ4644-4-4-4400400-4-4-4444-400000000000000000000000000000000000000000000−2i2i2i−2i000000
χ474-44-4000044i−4i40000-4-4000000004i−4i002-2002i−2i002-22-200002i−2i2i−2i0000000000000000000000
χ484-44-4000044i−4i40000-4-4000000004i−4i00-2200−2i2i00-22-220000−2i2i−2i2i0000000000000000000000
χ494-44-400004−4i4i40000-4-400000000−4i4i002-200−2i2i002-22-20000−2i2i−2i2i0000000000000000000000
χ504-44-400004−4i4i40000-4-400000000−4i4i00-22002i−2i00-22-2200002i−2i2i−2i0000000000000000000000
χ514-44-40000-24i−4i-2−2i32i3−2i32i32200000000−2i2i23−232-2002i−2i00−1−i31+i3−1+i31−i300002ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ524-44-40000-24i−4i-2−2i32i3−2i32i32200000000−2i2i23−23-2200−2i2i001+i3−1−i31−i3−1+i30000−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ534-44-40000-24i−4i-22i3−2i32i3−2i32200000000−2i2i−23232-2002i−2i00−1+i31−i3−1−i31+i300002ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ544-44-40000-24i−4i-22i3−2i32i3−2i32200000000−2i2i−2323-2200−2i2i001−i3−1+i31+i3−1−i30000−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ554-44-40000-2−4i4i-2−2i32i3−2i32i322000000002i−2i−23232-200−2i2i00−1−i31+i3−1+i31−i30000−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ564-44-40000-2−4i4i-2−2i32i3−2i32i322000000002i−2i−2323-22002i−2i001+i3−1−i31−i3−1+i300002ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ574-44-40000-2−4i4i-22i3−2i32i3−2i322000000002i−2i23−232-200−2i2i00−1+i31−i3−1−i31+i30000−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ584-44-40000-2−4i4i-22i3−2i32i3−2i322000000002i−2i23−23-22002i−2i001−i3−1+i31+i3−1−i300002ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ594-4-44004-4400-40000-4400004-4000000002-2002-200002-22-20000002-22-20000000000000000
χ604-4-44004-4400-40000-4400004-400000000-2200-220000-22-22000000-22-220000000000000000
χ614-4-44004-4-2002−2i32i32i3−2i32-20000-22−2i32i30000002-2002-20000−1−i31+i3−1+i31−i3000000−1−i31+i3−1+i31−i30000000000000000
χ624-4-44004-4-2002−2i32i32i3−2i32-20000-22−2i32i3000000-2200-2200001+i3−1−i31−i3−1+i30000001+i3−1−i31−i3−1+i30000000000000000
χ634-4-44004-4-20022i3−2i3−2i32i32-20000-222i3−2i30000002-2002-20000−1+i31−i3−1−i31+i3000000−1+i31−i3−1−i31+i30000000000000000
χ644-4-44004-4-20022i3−2i3−2i32i32-20000-222i3−2i3000000-2200-2200001−i3−1+i31+i3−1−i30000001−i3−1+i31+i3−1−i30000000000000000
χ654-4-4400-44400-40000-440000-44000000002-200-2200002-22-2000000-22-220000000000000000
χ664-4-4400-44400-40000-440000-4400000000-22002-20000-22-220000002-22-20000000000000000
χ674-4-4400-44-2002−2i32i32i3−2i32-200002-22i3−2i30000002-200-220000−1−i31+i3−1+i31−i30000001+i3−1−i31−i3−1+i30000000000000000
χ684-4-4400-44-2002−2i32i32i3−2i32-200002-22i3−2i3000000-22002-200001+i3−1−i31−i3−1+i3000000−1−i31+i3−1+i31−i30000000000000000
χ694-4-4400-44-20022i3−2i3−2i32i32-200002-2−2i32i30000002-200-220000−1+i31−i3−1−i31+i30000001−i3−1+i31+i3−1−i30000000000000000
χ704-4-4400-44-20022i3−2i3−2i32i32-200002-2−2i32i3000000-22002-200001−i3−1+i31+i3−1−i3000000−1+i31−i3−1−i31+i30000000000000000
χ7188-8-88-800-4004-4-444-44000000000000000000000000000000000000000000000000000000
χ7288-8-8-8800-400444-4-4-44000000000000000000000000000000000000000000000000000000

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