Finite Group Databasebeta

← Group #11778635

Character table — Group #11778635

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order12222233666666666634444666666666121212122666666661212121212121212121212121212244444446612121212121212121212121212128888
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
χ51111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ71111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111111111-1-111
χ81111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ9222222222222222222222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222220000000000000000000000000000
χ102222222222222222222-2-2-2-2222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ112222222-1222222-1-1-12-12222-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122220000-1-1-1-10000-1-1-1-100000000
χ122222222-1222222-1-1-12-12222-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011110000111100000000
χ132222222-1222222-1-1-12-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-222111111-1-1-1-100000000−i3i3−i3i30000−i3−i3i3i300000000
χ142222222-1222222-1-1-12-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-222111111-1-1-1-100000000i3−i3i3−i30000i3i3−i3−i300000000
χ152222222-1222222-1-1-12-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-211111122-2-2-1-1-1-1-1-111112-2-220000-1-1-1-10000111100000000
χ162222222-1222222-1-1-12-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-211111122-2-2-1-1-1-1-1-11111-222-2000011110000-1-1-1-100000000
χ172222222-1222222-1-1-12-1-2-2-2-2-1-1-1-1-1-1-1-1-11111222-1-1-1-1-1-1-2-2-2-2111111111100000000−i3i3−i3i30000i3i3−i3−i300000000
χ182222222-1222222-1-1-12-1-2-2-2-2-1-1-1-1-1-1-1-1-11111222-1-1-1-1-1-1-2-2-2-2111111111100000000i3−i3i3−i30000−i3−i3i3i300000000
χ19222222-12-1-1-1-1-1-1222-1-1222222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022220000-1-1-1-10000-1-1-1-10000
χ20222222-12-1-1-1-1-1-1222-1-1222222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-200001111000011110000
χ21222222-12-1-1-1-1-1-1222-1-122-2-222-1-1-1-1-1-1-12222-211-2-2111111-1-1-2-21111-1-1-1-1000000000000−i3−i3i3i30000−i3−i3i3i30000
χ22222222-12-1-1-1-1-1-1222-1-122-2-222-1-1-1-1-1-1-12222-211-2-2111111-1-1-2-21111-1-1-1-1000000000000i3i3−i3−i30000i3i3−i3−i30000
χ23222222-12-1-1-1-1-1-1222-1-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-2-21111-1-11122-1-1-1-11111000022-2-2000011110000-1-1-1-10000
χ24222222-12-1-1-1-1-1-1222-1-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-2-21111-1-11122-1-1-1-111110000-2-2220000-1-1-1-1000011110000
χ25222222-12-1-1-1-1-1-1222-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22-1-122-1-1-1-11111-2-211111111000000000000−i3−i3i3i30000i3i3−i3−i30000
χ26222222-12-1-1-1-1-1-1222-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22-1-122-1-1-1-11111-2-211111111000000000000i3i3−i3−i30000−i3−i3i3i30000
χ272222-2-222-2-222-2-222222002-2-2-22-2-2-2-22200000000000002-2002-222-2-2000002-200000000000002-22-200000000
χ282222-2-222-2-222-2-222222002-2-2-22-2-2-2-22200000000000002-2002-222-2-200000-220000000000000-22-2200000000
χ292222-2-222-2-222-2-22222200-22-2-22-2-2-2-2220000000000000-2200-22-2-2220000200-2000022-2-20000000000000000
χ302222-2-222-2-222-2-22222200-22-2-22-2-2-2-2220000000000000-2200-22-2-2220000-20020000-2-2220000000000000000
χ312222-2-22-1-2-222-2-2-1-1-12-1002-211-11111-1-1−i3−i3i3i3000−i3i3−i3−i3i3i32-200-11-1-111−i3−i3i3i302-200000−i3i3i3−i30000-11-1100000000
χ322222-2-22-1-2-222-2-2-1-1-12-1002-211-11111-1-1−i3−i3i3i3000−i3i3−i3−i3i3i32-200-11-1-111−i3−i3i3i30-2200000i3−i3−i3i300001-11-100000000
χ332222-2-22-1-2-222-2-2-1-1-12-1002-211-11111-1-1i3i3−i3−i3000i3−i3i3i3−i3−i32-200-11-1-111i3i3−i3−i302-200000i3−i3−i3i30000-11-1100000000
χ342222-2-22-1-2-222-2-2-1-1-12-1002-211-11111-1-1i3i3−i3−i3000i3−i3i3i3−i3−i32-200-11-1-111i3i3−i3−i30-2200000−i3i3i3−i300001-11-100000000
χ352222-2-22-1-2-222-2-2-1-1-12-100-2211-11111-1-1−i3−i3i3i3000i3−i3i3i3−i3−i3-22001-111-1-1−i3−i3i3i3200-20000-1-1110000−i3i3i3−i300000000
χ362222-2-22-1-2-222-2-2-1-1-12-100-2211-11111-1-1−i3−i3i3i3000i3−i3i3i3−i3−i3-22001-111-1-1−i3−i3i3i3-2002000011-1-10000i3−i3−i3i300000000
χ372222-2-22-1-2-222-2-2-1-1-12-100-2211-11111-1-1i3i3−i3−i3000−i3i3−i3−i3i3i3-22001-111-1-1i3i3−i3−i3200-20000-1-1110000i3−i3−i3i300000000
χ382222-2-22-1-2-222-2-2-1-1-12-100-2211-11111-1-1i3i3−i3−i3000−i3i3−i3−i3i3i3-22001-111-1-1i3i3−i3−i3-2002000011-1-10000−i3i3i3−i300000000
χ392-2-222-22222-2-2-2-22-2-2222i−2i002-2222-2-2-2-22i−2i2i−2i000000000002i−2i0000002i−2i2i−2i0000000000000000000000002−2−i2i2
χ402-2-222-22222-2-2-2-22-2-2222i−2i002-2222-2-2-2-22i−2i2i−2i000000000002i−2i0000002i−2i2i−2i000000000000000000000000−22i2−i2
χ412-2-222-22222-2-2-2-22-2-222−2i2i002-2222-2-2-2-2−2i2i−2i2i00000000000−2i2i000000−2i2i−2i2i0000000000000000000000002−2i2−i2
χ422-2-222-22222-2-2-2-22-2-222−2i2i002-2222-2-2-2-2−2i2i−2i2i00000000000−2i2i000000−2i2i−2i2i000000000000000000000000−22−i2i2
χ43444444-2-2-2-2-2-2-2-2-2-2-2-214444-2-21111111-2-2-2-24-2-2-2-21111-2-2-2-2-2-2111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2144-4-4-2-21111111-2-2-2-2-42222-1-1-1-122-2-222-1-1-1-111110000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-21-4-444-2-211111112222-42222-1-1-1-1-2-222-2-21111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-4-4-2-2111111122224-2-2-2-21111222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ474444-4-4-2422-2-222444-2-2004-4-4-4-22222-2-20000000000000-22004-4-2-22200000000000000000000000000000000
χ484444-4-4-2422-2-222444-2-200-44-4-4-22222-2-200000000000002-200-4422-2-200000000000000000000000000000000
χ494444-4-4-2-222-2-222-2-2-2-21004-4221-1-1-1-111−2i3−2i32i32i3000−2i32i3i3i3−i3−i3-2200-2211-1-1i3i3−i3−i30000000000000000000000000000
χ504444-4-4-2-222-2-222-2-2-2-21004-4221-1-1-1-1112i32i3−2i3−2i30002i3−2i3−i3−i3i3i3-2200-2211-1-1−i3−i3i3i30000000000000000000000000000
χ514444-4-4-2-222-2-222-2-2-2-2100-44221-1-1-1-111−2i3−2i32i32i30002i3−2i3−i3−i3i3i32-2002-2-1-111i3i3−i3−i30000000000000000000000000000
χ524444-4-4-2-222-2-222-2-2-2-2100-44221-1-1-1-1112i32i3−2i3−2i3000−2i32i3i3i3−i3−i32-2002-2-1-111−i3−i3i3i30000000000000000000000000000
χ5344-4-40044004-400-44-4-44000000-400004-40000000000000000000000000000000002i−2i00002i−2i2i−2i000000000000
χ5444-4-40044004-400-44-4-44000000-400004-4000000000000000000000000000000000−2i2i0000−2i2i−2i2i000000000000
χ5544-4-400-24−2i32i3-22−2i32i3-44-42-20000002−2i32i3−2i32i3-220000000000000000000000000000000002i−2i00002ζ14−2ζ142ζ22−2ζ22000000000000
χ5644-4-400-24−2i32i3-22−2i32i3-44-42-20000002−2i32i3−2i32i3-22000000000000000000000000000000000−2i2i0000−2ζ142ζ14−2ζ222ζ22000000000000
χ5744-4-400-242i3−2i3-222i3−2i3-44-42-200000022i3−2i32i3−2i3-220000000000000000000000000000000002i−2i00002ζ22−2ζ222ζ14−2ζ14000000000000
χ5844-4-400-242i3−2i3-222i3−2i3-44-42-200000022i3−2i32i3−2i3-22000000000000000000000000000000000−2i2i0000−2ζ222ζ22−2ζ142ζ14000000000000
χ594-44-4004400-4400-4-44-44000000-40000-4400000000000000000000000000000002i−2i000000000000002i−2i2i−2i0000
χ604-44-4004400-4400-4-44-44000000-40000-440000000000000000000000000000000−2i2i00000000000000−2i2i−2i2i0000
χ614-44-400-24−2i32i32-22i3−2i3-4-442-20000002−2i32i32i3−2i32-200000000000000000000000000000002i−2i000000000000002ζ14−2ζ142ζ22−2ζ220000
χ624-44-400-24−2i32i32-22i3−2i3-4-442-20000002−2i32i32i3−2i32-20000000000000000000000000000000−2i2i00000000000000−2ζ142ζ14−2ζ222ζ220000
χ634-44-400-242i3−2i32-2−2i32i3-4-442-200000022i3−2i3−2i32i32-200000000000000000000000000000002i−2i000000000000002ζ22−2ζ222ζ14−2ζ140000
χ644-44-400-242i3−2i32-2−2i32i3-4-442-200000022i3−2i3−2i32i32-20000000000000000000000000000000−2i2i00000000000000−2ζ222ζ22−2ζ142ζ140000
χ654-4-444-44-244-4-4-4-4-2224-24i−4i00-22-2-2-22222−2i2i−2i2i000000000004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ664-4-444-44-244-4-4-4-4-2224-2−4i4i00-22-2-2-222222i−2i2i−2i00000000000−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ674-4-444-4-24-2-222224-4-4-2-24i−4i004-4-2-2-222224i−4i4i−4i00000000000−2i2i000000−2i2i−2i2i0000000000000000000000000000
χ684-4-444-4-24-2-222224-4-4-2-2−4i4i004-4-2-2-22222−4i4i−4i4i000000000002i−2i0000002i−2i2i−2i0000000000000000000000000000
χ694-4-444-4-2-2-2-22222-222-214i−4i00-22111-1-1-1-1−2i2i−2i2i000003-33-300−2i2i003i−3i3i−3ii−ii−i0000000000000000000000000000
χ704-4-444-4-2-2-2-22222-222-214i−4i00-22111-1-1-1-1−2i2i−2i2i00000-33-3300−2i2i00−3i3i−3i3ii−ii−i0000000000000000000000000000
χ714-4-444-4-2-2-2-22222-222-21−4i4i00-22111-1-1-1-12i−2i2i−2i000003-33-3002i−2i00−3i3i−3i3i−ii−ii0000000000000000000000000000
χ724-4-444-4-2-2-2-22222-222-21−4i4i00-22111-1-1-1-12i−2i2i−2i00000-33-33002i−2i003i−3i3i−3i−ii−ii0000000000000000000000000000
χ734-4-44-4444-4-4-4-4444-4-4440000-444-4-444-4-40000000000000000000000000000000000000000000000000000000
χ744-4-44-444-2-4-4-4-444-2224-200002-2-222-2-22223−23−2323000000000000000000023−23−23230000000000000000000000000000
χ754-4-44-444-2-4-4-4-444-2224-200002-2-222-2-222−232323−230000000000000000000−232323−230000000000000000000000000000
χ764-4-44-44-242222-2-24-4-4-2-20000-44-222-2-22200000−2i32i300−2i32i32i3−2i3000000000000000000000000000000000000000000
χ774-4-44-44-242222-2-24-4-4-2-20000-44-222-2-222000002i3−2i3002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ784-4-44-44-2-22222-2-2-222-2100002-21-1-111-1-123−23−23230−2i32i300i3−i3−i3i3000000−3i3i3i−3i−333−30000000000000000000000000000
χ794-4-44-44-2-22222-2-2-222-2100002-21-1-111-1-123−23−232302i3−2i300−i3i3i3−i30000003i−3i−3i3i−333−30000000000000000000000000000
χ804-4-44-44-2-22222-2-2-222-2100002-21-1-111-1-1−232323−230−2i32i300i3−i3−i3i30000003i−3i−3i3i3−3−330000000000000000000000000000
χ814-4-44-44-2-22222-2-2-222-2100002-21-1-111-1-1−232323−2302i3−2i300−i3i3i3−i3000000−3i3i3i−3i3−3−330000000000000000000000000000
χ8288-8-8008-4008-8004-44-8-400000040000-440000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4−4i34i3-44−4i34i34-4442000000-22i3−2i32i3−2i32-20000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-44i3−4i3-444i3−4i34-4442000000-2−2i32i3−2i32i32-20000000000000000000000000000000000000000000000000000000
χ858-88-8008-400-880044-4-8-4000000400004-40000000000000000000000000000000000000000000000000000000
χ868-88-800-4-4−4i34i34-44i3−4i344-442000000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000
χ878-88-800-4-44i3−4i34-4−4i34i344-442000000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000

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