Finite Group Databasebeta

← Group #11778479

Character table — Group #11778479

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222244444444444488888888888888812121212121216161616161624242424242424242424242424242424242424242472727272
order122222336666663446666666121244661212121212121212121212226666121212121212444448812121212121212121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1111111-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ611111111111111111111111111-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-111-1-11111-1-111
χ711111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111111-1-111-1-1-1-1-1-111
χ811111111111111111111111111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1-1-111111111-1-1
χ9222222222222222-2-22222222-2-20022-2-2-20000-2-2-2-2222222000000000-2000000000-2-20000000000
χ10222222222222222-2-22222222-2-20022-2-2-20000-2-2-2-2-2-2-2-2-2-20000000002000000000220000000000
χ112222222-1-122-12-1-12222-1-1-1-1-12222-1-12-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12002200-1-10000-1-1-1-100000000
χ122222222-1-122-12-1-12222-1-1-1-1-12222-1-12-1-1-1-1-1-1-1-1-1-1-2-2111122-1-1-1-1-200-2-200110000111100000000
χ132222222-1-122-12-1-12222-1-1-1-1-122-2-2-1-12-1-11111-1-1-1-122-1-1-1-1-2-21111-2002-200110000-1-11100000000
χ142222222-1-122-12-1-12222-1-1-1-1-122-2-2-1-12-1-11111-1-1-1-1-2-21111-2-21111200-2200-1-1000011-1-100000000
χ152222222-1-122-12-1-1-2-222-1-1-1-1-1-2-200-1-1-211−i3i3−i3i3111122-1-1-1-100−i3i3−i3i3000-2000−i3i3000011−i3i300000000
χ162222222-1-122-12-1-1-2-222-1-1-1-1-1-2-200-1-1-211−i3i3−i3i31111-2-2111100−i3i3−i3i30002000i3−i30000-1-1i3−i300000000
χ172222222-1-122-12-1-1-2-222-1-1-1-1-1-2-200-1-1-211i3−i3i3−i3111122-1-1-1-100i3−i3i3−i3000-2000i3−i3000011i3−i300000000
χ182222222-1-122-12-1-1-2-222-1-1-1-1-1-2-200-1-1-211i3−i3i3−i31111-2-2111100i3−i3i3−i30002000−i3i30000-1-1−i3i300000000
χ19222222-122-1-12-12-122-1-122-1-1-1-1-122-1-1-1222222-1-1-1-1000000-1-1-1-1-1-1022002200-1-1-1-10000-1-1-1-10000
χ20222222-122-1-12-12-122-1-122-1-1-1-1-122-1-1-1222222-1-1-1-1000000-1-1-1-1-1-10-2-200-2-2001111000011110000
χ21222222-122-1-12-12-122-1-122-1-1-1-1-1-2-2-1-1-122-2-2-2-2-1-1-1-100000011111102200-2-200-1-1-1-1000011110000
χ22222222-122-1-12-12-122-1-122-1-1-1-1-1-2-2-1-1-122-2-2-2-2-1-1-1-10000001111110-2-200220011110000-1-1-1-10000
χ232222-2-22222222222-2-2-2-2-2222222-2-2-2-22-222-2-222-2-2000000-22-2-2220000000000000000000000000
χ242222-2-22222222222-2-2-2-2-222222-22-2-2-22-2-2-22222-2-20000002-222-2-20000000000000000000000000
χ252222-2-2222222222-22-2-2-2-2222-2-200-2-22-220000-2-2220000000000002000-20022000000-2-200000000
χ262222-2-2222222222-22-2-2-2-2222-2-200-2-22-220000-2-222000000000000-2000200-2-20000002200000000
χ272222-2-22-1-122-12-1-12-2-2-211-1-1-1222-211-2-11-1-111-1-11100−i3−i3i3i3-2211-1-10000000−i3i30000−i3i3i3−i300000000
χ282222-2-22-1-122-12-1-12-2-2-211-1-1-1222-211-2-11-1-111-1-11100i3i3−i3−i3-2211-1-10000000i3−i30000i3−i3−i3i300000000
χ292222-2-22-1-122-12-1-12-2-2-211-1-1-122-2211-2-1111-1-1-1-11100−i3−i3i3i32-2-1-1110000000i3−i30000−i3i3−i3i300000000
χ302222-2-22-1-122-12-1-12-2-2-211-1-1-122-2211-2-1111-1-1-1-11100i3i3−i3−i32-2-1-1110000000−i3i30000i3−i3i3−i300000000
χ312222-2-22-1-122-12-1-1-22-2-211-1-1-1-2-2001121-1−i3i3i3−i311-1-100−i3−i3i3i300i3−i3−i3i32000-200-1-10000i3−i31100000000
χ322222-2-22-1-122-12-1-1-22-2-211-1-1-1-2-2001121-1−i3i3i3−i311-1-100i3i3−i3−i300i3−i3−i3i3-2000200110000−i3i3-1-100000000
χ332222-2-22-1-122-12-1-1-22-2-211-1-1-1-2-2001121-1i3−i3−i3i311-1-100−i3−i3i3i300−i3i3i3−i3-2000200110000i3−i3-1-100000000
χ342222-2-22-1-122-12-1-1-22-2-211-1-1-1-2-2001121-1i3−i3−i3i311-1-100i3i3−i3−i300−i3i3i3−i32000-200-1-10000−i3i31100000000
χ352222-2-2-122-1-12-12-12-211-2-2-1-1-1-1-12-21112-222-2-2-1-1110000001-111-1-1000000000−i3−i3i3i30000−i3−i3i3i30000
χ362222-2-2-122-1-12-12-12-211-2-2-1-1-1-1-12-21112-222-2-2-1-1110000001-111-1-1000000000i3i3−i3−i30000i3i3−i3−i30000
χ372222-2-2-122-1-12-12-12-211-2-2-1-1-1-1-1-221112-2-2-222-1-111000000-11-1-111000000000−i3−i3i3i30000i3i3−i3−i30000
χ382222-2-2-122-1-12-12-12-211-2-2-1-1-1-1-1-221112-2-2-222-1-111000000-11-1-111000000000i3i3−i3−i30000−i3−i3i3i30000
χ392-22-2-22222-2-2-22-22002-22-22-2-200002-2000000000002-22-22-200000000000−i2i20000000000−i2i2−i2i200−i2i2
χ402-22-2-22222-2-2-22-22002-22-22-2-200002-2000000000002-22-22-200000000000i2−i20000000000i2−i2i2−i200i2−i2
χ412-22-2-22222-2-2-22-22002-22-22-2-200002-200000000000-22-22-2200000000000−i2i20000000000−i2i2−i2i200i2−i2
χ422-22-2-22222-2-2-22-22002-22-22-2-200002-200000000000-22-22-2200000000000i2−i20000000000i2−i2i2−i200−i2i2
χ43444444-244-2-24-24-2-4-4-2-244-2-2-22200-2-22-4-4000022220000000000000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2144-2-2-2-2111-2-24411-2-2-2-2-2-2-21111000000-2-211110000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2144-2-2-2-2111-2-2-4-411-2-2-22222111100000022-1-1-1-10000000000000000000000000
χ46444444-2-2-2-2-2-2-2-21-4-4-2-2-2-2111220011222−2i32i3−2i32i3-1-1-1-100000000i3−i3i3−i30000000000000000000000000
χ47444444-2-2-2-2-2-2-2-21-4-4-2-2-2-21112200112222i3−2i32i3−2i3-1-1-1-100000000−i3i3−i3i30000000000000000000000000
χ484444-4-4-244-2-24-24-2-4422-4-4-2-2-2220022-2-44000022-2-20000000000000000000000000000000000000
χ494444-4-4-2-2-2-2-2-2-2-214-42222111-2-24-4-1-12-22-2-22211-1-10000002-2-1-1110000000000000000000000000
χ504444-4-4-2-2-2-2-2-2-2-214-42222111-2-2-44-1-12-2222-2-211-1-1000000-2211-1-10000000000000000000000000
χ514444-4-4-2-2-2-2-2-2-2-21-4422221112200-1-1-22-2−2i32i32i3−2i3-1-11100000000−i3i3i3−i30000000000000000000000000
χ524444-4-4-2-2-2-2-2-2-2-21-4422221112200-1-1-22-22i3−2i3−2i32i3-1-11100000000i3−i3−i3i30000000000000000000000000
χ5344-4-40044-4-444-4-44000000-4-440000000000000000000000000000002i−2i0000002i−2i2i−2i000000000000
χ5444-4-40044-4-444-4-44000000-4-44000000000000000000000000000000−2i2i000000−2i2i−2i2i000000000000
χ5544-4-400-24-42-242-4-200000022-2−2i32i300000000000−2i32i30000000000000002i−2i0000002ζ14−2ζ142ζ22−2ζ22000000000000
χ5644-4-400-24-42-242-4-200000022-2−2i32i300000000000−2i32i3000000000000000−2i2i000000−2ζ142ζ14−2ζ222ζ22000000000000
χ5744-4-400-24-42-242-4-200000022-22i3−2i3000000000002i3−2i30000000000000002i−2i0000002ζ22−2ζ222ζ14−2ζ14000000000000
χ5844-4-400-24-42-242-4-200000022-22i3−2i3000000000002i3−2i3000000000000000−2i2i000000−2ζ222ζ22−2ζ142ζ14000000000000
χ594-44-44-4444-4-4-44-4400-44-444-4-40000-44000000000000000000000000000000000000000000000000
χ604-44-44-44-2-2-4-4242-200-442-2-22200002-20000000000000−2i32i32i3−2i30000000000000000000000000000000
χ614-44-44-44-2-2-4-4242-200-442-2-22200002-200000000000002i3−2i3−2i32i30000000000000000000000000000000
χ624-44-44-4-24422-4-2-4-2002-2-44-22200002-200000000000000000000000000000000000000006−6−660000
χ634-44-44-4-24422-4-2-4-2002-2-44-22200002-20000000000000000000000000000000000000000−666−60000
χ644-44-4-444-2-2-4-4242-2004-4-22-2220000-22000000000004-4-22-220000000000000000000000000000000
χ654-44-4-444-2-2-4-4242-2004-4-22-2220000-2200000000000-442-22-20000000000000000000000000000000
χ664-44-4-44-24422-4-2-4-200-224-4-2220000-220000000000000000000000000000−2i22i20000000000i2−i2i2−i20000
χ674-44-4-44-24422-4-2-4-200-224-4-2220000-2200000000000000000000000000002i2−2i20000000000−i2i2−i2i20000
χ684-4-440044-44-4-4-444000000-44-4000000000000000000000000000000000000000000000000002i−2i00
χ694-4-440044-44-4-4-444000000-44-400000000000000000000000000000000000000000000000000−2i2i00
χ7088-8-8008-44-88-4-84-400000044-4000000000000000000000000000000000000000000000000000000
χ7188-8-800-4-444-4-4442000000-2-22−4i34i3000000000002i3−2i3000000000000000000000000000000000000000
χ7288-8-800-4-444-4-4442000000-2-224i3−4i300000000000−2i32i3000000000000000000000000000000000000000
χ738-88-88-8-4-4-4444-442004-44-42-2-20000-22000000000000000000000000000000000000000000000000
χ748-88-8-88-4-4-4444-44200-44-442-2-200002-2000000000000000000000000000000000000000000000000
χ758-8-88008-448-84-8-4-40000004-44000000000000000000000000000000000000000000000000000000
χ768-8-8800-48-8-44-848-40000004-44000000000000000000000000000000000000000000000000000000
χ778-8-8800-4-44-4444-42000000-22-20000000000000006i−6i0000000000000000000000000000000000000
χ788-8-8800-4-44-4444-42000000-22-2000000000000000−6i6i0000000000000000000000000000000000000

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