Finite Group Databasebeta

← Group #11778224

Character table — Group #11778224

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order1222223366666666662234466666666666664666666121212121212121212121212121212122244444466661212121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-111111-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11-11-111-1-111-1-1-1-1-1-111-1-1111111-1-1
χ6111111111111111111-1-111111-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11-11-1-1-11111-1-1111111-1-1-1-1-1-1-1-111
χ7111111111111111111-1-111111-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-11-1111-1-1-1-111-1-1-1-1-1-1111111-1-111
χ8111111111111111111-1-111111-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-11-11-1-111-1-1111111-1-111-1-1-1-111-1-1
χ9222222222222222222222-2-22222222222222-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222222222222222-2-22-2-222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000000000000000
χ112222222-12222-1-122-1222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122220000-1-1-1-10000-1-1-1-100000000
χ122222222-12222-1-122-1222-122-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-2000011110000111100000000
χ132222222-12222-1-122-1222-1-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-1-1-1-111-2-211-2-21111111100000000−i3i3−i3i30000−i3i3−i3i300000000
χ142222222-12222-1-122-1222-1-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-1-1-1-111-2-211-2-21111111100000000i3−i3i3−i30000i3−i3i3−i300000000
χ152222222-12222-1-122-12-2-2-122-1-11111-1-1-1-1-1-1-1-2-2-21111-1-1-2-21122-1-1-1-111112-22-20000-1-1110000-1-11100000000
χ162222222-12222-1-122-12-2-2-122-1-11111-1-1-1-1-1-1-1-2-2-21111-1-1-2-21122-1-1-1-11111-22-22000011-1-1000011-1-100000000
χ172222222-12222-1-122-12-2-2-1-2-2-1-11111-1-1-1-1-1-1-12-2-211111122-1-1-2-21111-1-1-1-100000000−i3i3i3−i30000−i3i3i3−i300000000
χ182222222-12222-1-122-12-2-2-1-2-2-1-11111-1-1-1-1-1-1-12-2-211111122-1-1-2-21111-1-1-1-100000000i3−i3−i3i30000i3−i3−i3i300000000
χ19222222-12-1-1-1-122-1-12-122-122222222-1-1-1-1-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1000022220000-1-1-1-10000-1-1-1-10000
χ20222222-12-1-1-1-122-1-12-122-122222222-1-1-1-1-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-200001111000011110000
χ21222222-12-1-1-1-122-1-12-122-1-2-2222222-1-1-1-1-1-1-1-2-1-1-1-1-1-1-2-211-2-21111111111000000000000−i3−i3i3i30000−i3−i3i3i30000
χ22222222-12-1-1-1-122-1-12-122-1-2-2222222-1-1-1-1-1-1-1-2-1-1-1-1-1-1-2-211-2-21111111111000000000000i3i3−i3−i30000i3i3−i3−i30000
χ23222222-12-1-1-1-122-1-12-1-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-21111112211-2-2-1-1-1-1-1-11111000022-2-2000011110000-1-1-1-10000
χ24222222-12-1-1-1-122-1-12-1-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-21111112211-2-2-1-1-1-1-1-111110000-2-2220000-1-1-1-1000011110000
χ25222222-12-1-1-1-122-1-12-1-2-2-1-2-222-2-2-2-2-1-1-1-1-1-1-12111111-2-2-1-122111111-1-1-1-1000000000000−i3−i3i3i30000i3i3−i3−i30000
χ26222222-12-1-1-1-122-1-12-1-2-2-1-2-222-2-2-2-2-1-1-1-1-1-1-12111111-2-2-1-122111111-1-1-1-1000000000000i3i3−i3−i30000−i3−i3i3i30000
χ272222-2-2222-2-2222-2-2220022-2-2-200002-2-2-2-22200000002-200002-222-2-20000020-200000022000000-2-200000000
χ282222-2-2222-2-2222-2-2220022-2-2-200002-2-2-2-22200000002-200002-222-2-200000-202000000-2-20000002200000000
χ292222-2-2222-2-2222-2-222002-22-2-200002-2-2-2-2220000000-220000-22-2-222000020-20000022000000-2-20000000000
χ302222-2-2222-2-2222-2-222002-22-2-200002-2-2-2-2220000000-220000-22-2-2220000-20200000-2-2000000220000000000
χ312222-2-22-12-2-22-1-1-2-2-1200-12-211−i3−i3i3i3-11111-1-1000−i3−i3i3i3-1100−i3i32-2-1-111−i3−i3i3i3020-20000−i3i3-1-10000i3−i31100000000
χ322222-2-22-12-2-22-1-1-2-2-1200-12-211−i3−i3i3i3-11111-1-1000−i3−i3i3i3-1100−i3i32-2-1-111−i3−i3i3i30-2020000i3−i3110000−i3i3-1-100000000
χ332222-2-22-12-2-22-1-1-2-2-1200-12-211i3i3−i3−i3-11111-1-1000i3i3−i3−i3-1100i3−i32-2-1-111i3i3−i3−i3020-20000i3−i3-1-10000−i3i31100000000
χ342222-2-22-12-2-22-1-1-2-2-1200-12-211i3i3−i3−i3-11111-1-1000i3i3−i3−i3-1100i3−i32-2-1-111i3i3−i3−i30-2020000−i3i3110000i3−i3-1-100000000
χ352222-2-22-12-2-22-1-1-2-2-1200-1-2211−i3−i3i3i3-11111-1-1000−i3−i3i3i31-100i3−i3-2211-1-1i3i3−i3−i320-200000-1-1−i3i3000011i3−i300000000
χ362222-2-22-12-2-22-1-1-2-2-1200-1-2211−i3−i3i3i3-11111-1-1000−i3−i3i3i31-100i3−i3-2211-1-1i3i3−i3−i3-2020000011i3−i30000-1-1−i3i300000000
χ372222-2-22-12-2-22-1-1-2-2-1200-1-2211i3i3−i3−i3-11111-1-1000i3i3−i3−i31-100−i3i3-2211-1-1−i3−i3i3i320-200000-1-1i3−i3000011−i3i300000000
χ382222-2-22-12-2-22-1-1-2-2-1200-1-2211i3i3−i3−i3-11111-1-1000i3i3−i3−i31-100−i3i3-2211-1-1−i3−i3i3i3-2020000011−i3i30000-1-1i3−i300000000
χ392-22-22-222222-2-2-2-2-22-22-22002-22-22-2222-2-2-2-202-22-22-20000000000000000000000000000000000000000−i2i2−i2i2
χ402-22-22-222222-2-2-2-2-22-22-22002-22-22-2222-2-2-2-202-22-22-20000000000000000000000000000000000000000i2−i2i2−i2
χ412-22-22-222222-2-2-2-2-22-2-222002-2-22-22222-2-2-2-20-22-22-220000000000000000000000000000000000000000−i2i2i2−i2
χ422-22-22-222222-2-2-2-2-22-2-222002-2-22-22222-2-2-2-20-22-22-220000000000000000000000000000000000000000i2−i2−i2i2
χ43444444-2-2-2-2-2-2-2-2-2-2-2-244144-2-2-2-2-2-211111114-2-21111-2-2-2-2-2-2-2-2111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2441-4-4-2-2-2-2-2-21111111-4-2-2111122222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-2-4-4144-2-222221111111-422-1-1-1-1-2-22222-2-21111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-2-4-41-4-4-2-222221111111422-1-1-1-122-2-2-2-222-1-1-1-111110000000000000000000000000000
χ474444-4-4-24-222-244224-200-24-4-4-40000-22222-2-200000004-40000-22-2-22200000000000000000000000000000000
χ484444-4-4-24-222-244224-200-2-44-4-40000-22222-2-20000000-4400002-222-2-200000000000000000000000000000000
χ494444-4-4-2-2-222-2-2-222-2-20014-422−2i3−2i32i32i31-1-1-1-111000i3i3−i3−i3-2200−2i32i3-2211-1-1i3i3−i3−i30000000000000000000000000000
χ504444-4-4-2-2-222-2-2-222-2-20014-4222i32i3−2i3−2i31-1-1-1-111000−i3−i3i3i3-22002i3−2i3-2211-1-1−i3−i3i3i30000000000000000000000000000
χ514444-4-4-2-2-222-2-2-222-2-2001-4422−2i3−2i32i32i31-1-1-1-111000i3i3−i3−i32-2002i3−2i32-2-1-111−i3−i3i3i30000000000000000000000000000
χ524444-4-4-2-2-222-2-2-222-2-2001-44222i32i3−2i3−2i31-1-1-1-111000−i3−i3i3i32-200−2i32i32-2-1-111i3i3−i3−i30000000000000000000000000000
χ5344-4-40044-40044-400-4-400400000000-400004-4000000000000000000000000000002i−2i00002i−2i2i−2i000000000000
χ5444-4-40044-40044-400-4-400400000000-400004-400000000000000000000000000000−2i2i0000−2i2i−2i2i000000000000
χ5544-4-400-242−2i32i3-24-4−2i32i3-4200-2000000002−2i32i3−2i32i3-22000000000000000000000000000002i−2i00002ζ14−2ζ142ζ22−2ζ22000000000000
χ5644-4-400-242−2i32i3-24-4−2i32i3-4200-2000000002−2i32i3−2i32i3-2200000000000000000000000000000−2i2i0000−2ζ142ζ14−2ζ222ζ22000000000000
χ5744-4-400-2422i3−2i3-24-42i3−2i3-4200-20000000022i3−2i32i3−2i3-22000000000000000000000000000002i−2i00002ζ22−2ζ222ζ14−2ζ14000000000000
χ5844-4-400-2422i3−2i3-24-42i3−2i3-4200-20000000022i3−2i32i3−2i3-2200000000000000000000000000000−2i2i0000−2ζ222ζ22−2ζ142ζ14000000000000
χ594-44-44-44-2444-422-4-4-2-44-4-200-22-22-22-2-2-2222204-4-22-2200000000000000000000000000000000000000000000
χ604-44-44-44-2444-422-4-4-2-4-44-200-222-22-2-2-2-222220-442-22-200000000000000000000000000000000000000000000
χ614-44-44-4-24-2-2-22-4-422424-4-2004-44-44-4-2-2-222220-22-22-2200000000000000000000000000000000000000000000
χ624-44-44-4-24-2-2-22-4-42242-44-2004-4-44-44-2-2-2222202-22-22-200000000000000000000000000000000000000000000
χ634-44-44-4-2-2-2-2-222222-224-4100-22-22-22111-1-1-1-10-221-11-1000000003i−3i3i−3i3i−3i3i−3i0000000000000000000000000000
χ644-44-44-4-2-2-2-2-222222-224-4100-22-22-22111-1-1-1-10-221-11-100000000−3i3i−3i3i−3i3i−3i3i0000000000000000000000000000
χ654-44-44-4-2-2-2-2-222222-22-44100-222-22-2111-1-1-1-102-2-11-11000000003i−3i3i−3i−3i3i−3i3i0000000000000000000000000000
χ664-44-44-4-2-2-2-2-222222-22-44100-222-22-2111-1-1-1-102-2-11-1100000000−3i3i−3i3i3i−3i3i−3i0000000000000000000000000000
χ674-44-4-44444-4-4-4-4-4444-400400-4400004-4-444-4-4000000000000000000000000000000000000000000000000000
χ684-44-4-444-24-4-4-42244-2-400-2002-2−2i32i32i3−2i3-222-2-222000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ694-44-4-444-24-4-4-42244-2-400-2002-22i3−2i3−2i32i3-222-2-2220002i3−2i3−2i32i300000000000000000000000000000000000000000000
χ704-44-4-44-24-2222-4-4-2-24200-200-440000-222-2-22200000000023−230000000023−23−23230000000000000000000000000000
χ714-44-4-44-24-2222-4-4-2-24200-200-440000-222-2-222000000000−232300000000−232323−230000000000000000000000000000
χ724-44-4-44-2-2-222222-2-2-22001002-2−2i32i32i3−2i31-1-111-1-1000i3−i3−i3i30023−230000−3i3i3i−3i−333−30000000000000000000000000000
χ734-44-4-44-2-2-222222-2-2-22001002-2−2i32i32i3−2i31-1-111-1-1000i3−i3−i3i300−232300003i−3i−3i3i3−3−330000000000000000000000000000
χ744-44-4-44-2-2-222222-2-2-22001002-22i3−2i3−2i32i31-1-111-1-1000−i3i3i3−i30023−2300003i−3i−3i3i−333−30000000000000000000000000000
χ754-44-4-44-2-2-222222-2-2-22001002-22i3−2i3−2i32i31-1-111-1-1000−i3i3i3−i300−23230000−3i3i3i−3i3−3−330000000000000000000000000000
χ764-4-440044-400-4-4400-4400400000000-40000-440000000000000000000000000002-2000000000000002-22-20000
χ774-4-440044-400-4-4400-4400400000000-40000-44000000000000000000000000000-2200000000000000-22-220000
χ784-4-4400-242−2i32i32-442i3−2i3-4-200-2000000002−2i32i32i3−2i32-20000000000000000000000000002-200000000000000−1+i31−i3−1−i31+i30000
χ794-4-4400-242−2i32i32-442i3−2i3-4-200-2000000002−2i32i32i3−2i32-2000000000000000000000000000-22000000000000001−i3−1+i31+i3−1−i30000
χ804-4-4400-2422i3−2i32-44−2i32i3-4-200-20000000022i3−2i3−2i32i32-20000000000000000000000000002-200000000000000−1−i31+i3−1+i31−i30000
χ814-4-4400-2422i3−2i32-44−2i32i3-4-200-20000000022i3−2i3−2i32i32-2000000000000000000000000000-22000000000000001+i3−1−i31−i3−1+i30000
χ8288-8-8008-4-8008-44004-800-40000000040000-44000000000000000000000000000000000000000000000000000
χ8388-8-800-4-44−4i34i3-4-44−4i34i34400200000000-22i3−2i32i3−2i32-2000000000000000000000000000000000000000000000000000
χ8488-8-800-4-444i3−4i3-4-444i3−4i34400200000000-2−2i32i3−2i32i32-2000000000000000000000000000000000000000000000000000
χ858-8-88008-4-800-84-4004800-400000000400004-4000000000000000000000000000000000000000000000000000
χ868-8-8800-4-44−4i34i344-44i3−4i34-400200000000-22i3−2i3−2i32i3-22000000000000000000000000000000000000000000000000000
χ878-8-8800-4-444i3−4i344-4−4i34i34-400200000000-2−2i32i32i3−2i3-22000000000000000000000000000000000000000000000000000

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