Finite Group Databasebeta

← Group #72252794

Character table — Group #72252794

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11222244444488888888999916161616181818181818181818181818181836363636363636363636363636363636363636363636363636363636363672727272727272728181162162
order12336633366633336666222233664444444444666666666612121212121212121212121212121212121212121212121212121212121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ31111111111111111111111111111-1-1-1-11111-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-11111111-1-111-1-11111111-1-1-1-1111-1-111-1-111-1-111-1-11111111111-1-111-1-1-1-1-1-1
χ6111111111111111111111-1-11111111-1-1-1-111-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ7111111111111111111111-1-111111-1-11111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111-1-111111-1-111-1-1111111111-1-1-1-11-1-111-1-111-1-111-1-11111111111-1-111-1-111-1-1-1-1
χ91-111-1-1111-1-1-11111-1-1-1-1-11-1111-1-1i−ii−ii−ii−i1-1-1-111-111-1-11i−ii−ii−ii−ii−ii−ii−ii−i11-1-111-1-1i−ii−ii−ii−i1-11-1
χ101-111-1-1111-1-1-11111-1-1-1-1-11-1111-1-1i−ii−i−ii−ii-11-1-111-111-1-11i−ii−i−ii−iii−ii−i−ii−ii-1-111-1-111i−ii−i−ii−ii1-1-11
χ111-111-1-1111-1-1-11111-1-1-1-1-11-1111-1-1−ii−iii−ii−i-11-1-111-111-1-11−ii−iii−ii−i−ii−iii−ii−i-1-111-1-111−ii−iii−ii−i1-1-11
χ121-111-1-1111-1-1-11111-1-1-1-1-11-1111-1-1−ii−ii−ii−ii1-1-1-111-111-1-11−ii−ii−ii−ii−ii−ii−ii−ii11-1-111-1-1−ii−ii−ii−ii1-11-1
χ131-111-1-1111-1-1-11111-1-1-1-1-1-11111-1-1i−i−iii−i−ii1-1-1-111-1-1-1111i−i−iii−i−iii−i−iii−i−ii11-1-111-1-1i−i−iii−i−ii-11-11
χ141-111-1-1111-1-1-11111-1-1-1-1-1-11111-1-1i−i−ii−iii−i-11-1-111-1-1-1111i−i−ii−iii−ii−i−ii−iii−i-1-111-1-111i−i−ii−iii−i-111-1
χ151-111-1-1111-1-1-11111-1-1-1-1-1-11111-1-1−iii−ii−i−ii-11-1-111-1-1-1111−iii−ii−i−ii−iii−ii−i−ii-1-111-1-111−iii−ii−i−ii-111-1
χ161-111-1-1111-1-1-11111-1-1-1-1-1-11111-1-1−iii−i−iii−i1-1-1-111-1-1-1111−iii−i−iii−i−iii−i−iii−i11-1-111-1-1−iii−i−iii−i-11-11
χ1722222222222222222222-222-222220000000000-2-2-2-2-22222-200000000000000000000000000000000-2-200
χ1822222222222222222222-2-2-2-222220000000000-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002200
χ19222-12-122-1-12222-1-122-1-12002-1-1-1-100220022222-12-1-10000-100-1-100-1-1002200222-12-1-1-1-1-100-1-100-1-10000
χ20222-12-122-1-12222-1-122-1-12002-1-1-1-1002200-2-2-2-22-12-1-10000-100-1-10011002200-2-2-21-21111100-1-100110000
χ21222-12-122-1-12222-1-122-1-12002-1-1-1-100-2-20022-2-22-12-1-10000-1001100-1-100-2-20022-21-211111001100-1-10000
χ22222-12-122-1-12222-1-122-1-12002-1-1-1-100-2-200-2-2222-12-1-10000-10011001100-2-200-2-22-12-1-1-1-1-1001100110000
χ2322-12-1222-1-122-1-122-1-1222002-1-1-1-12200220022-12-12-10000-1-1-100-1-10022002200-12-12-1-1-1-1-1-100-1-1000000
χ2422-12-1222-1-122-1-122-1-1222002-1-1-1-12200-2-200-2-2-12-12-10000-1-1-10011002200-2-2001-21-21111-1-10011000000
χ2522-12-1222-1-122-1-122-1-1222002-1-1-1-1-2-2002200-2-2-12-12-10000-11100-1-100-2-20022001-21-211111100-1-1000000
χ2622-12-1222-1-122-1-122-1-1222002-1-1-1-1-2-200-2-20022-12-12-10000-111001100-2-200-2-200-12-12-1-1-1-1110011000000
χ272-222-2-2222-2-2-22222-2-2-2-222-2-222-2-2000000000022-2-2222-2-2-200000000000000000000000000000000-2200
χ282-222-2-2222-2-2-22222-2-2-2-22-22-222-2-2000000000022-2-22-2-222-2000000000000000000000000000000002-200
χ292-22-1-2122-11-2-222-1-1-2-211-2002-1-111002i−2i002i−2i2-2-212-110000-100−ii00−ii002i−2i002i−2i2-1-21-1-11100−ii00−ii0000
χ302-22-1-2122-11-2-222-1-1-2-211-2002-1-111002i−2i00−2i2i-22-212-110000-100−ii00i−i002i−2i00−2i2i-212-111-1-100−ii00i−i0000
χ312-22-1-2122-11-2-222-1-1-2-211-2002-1-11100−2i2i002i−2i-22-212-110000-100i−i00−ii00−2i2i002i−2i-212-111-1-100i−i00−ii0000
χ322-22-1-2122-11-2-222-1-1-2-211-2002-1-11100−2i2i00−2i2i2-2-212-110000-100i−i00i−i00−2i2i00−2i2i2-1-21-1-11100i−i00i−i0000
χ332-2-121-222-11-2-2-1-12211-2-2-2002-1-1112i−2i002i−2i002-21-2-1210000-1−ii00−ii002i−2i002i−2i00-121-2-1-111−ii00−ii000000
χ342-2-121-222-11-2-2-1-12211-2-2-2002-1-1112i−2i00−2i2i00-221-2-1210000-1−ii00i−i002i−2i00−2i2i001-2-1211-1-1−ii00i−i000000
χ352-2-121-222-11-2-2-1-12211-2-2-2002-1-111−2i2i002i−2i00-221-2-1210000-1i−i00−ii00−2i2i002i−2i001-2-1211-1-1i−i00−ii000000
χ362-2-121-222-11-2-2-1-12211-2-2-2002-1-111−2i2i00−2i2i002-21-2-1210000-1i−i00i−i00−2i2i00−2i2i00-121-2-1-111i−i00i−i000000
χ374444441-2441-21-21-21-21-204401-21-20000222200000001-21-20000022220000-1-1-1-1000000000000-1-1-1-10000
χ384444441-2441-21-21-21-21-204401-21-20000-2-2-2-200000001-21-200000-2-2-2-20000111100000000000011110000
χ394444441-2441-21-21-21-21-20-4-401-21-2000022-2-20000000-12-120000022-2-20000-1-111000000000000-1-1110000
χ404444441-2441-21-21-21-21-20-4-401-21-20000-2-2220000000-12-1200000-2-222000011-1-100000000000011-1-10000
χ41444444-2144-21-21-21-21-210440-21-21222200000000000-21-21022220000-1-1-1-1000000000000-1-1-1-100000000
χ42444444-2144-21-21-21-21-210440-21-21-2-2-2-200000000000-21-210-2-2-2-200001111000000000000111100000000
χ43444444-2144-21-21-21-21-210-4-40-21-2122-2-2000000000002-12-1022-2-20000-1-111000000000000-1-11100000000
χ44444444-2144-21-21-21-21-210-4-40-21-21-2-222000000000002-12-10-2-222000011-1-100000000000011-1-100000000
χ45444-24-244-2-24444-2-244-2-2-400-4-2-2-2-20000000000-42-42200002000000000000000000000000000000000000
χ4644-24-2444-2-244-2-244-2-244-400-4-2-2-2-200000000002-42-4200002000000000000000000000000000000000000
χ4744-2-2-2-2441144-2-2-2-2-2-2-2-2400411110000000044-2-2-2-21000010000000000000000-2-2-2-21111000000000000
χ4844-2-2-2-2441144-2-2-2-2-2-2-2-24004111100000000-4-4-2-2-2-210000100000000000000002222-1-1-1-1000000000000
χ4944-2-2-2-2441144-2-2-2-2-2-2-2-2-400-4111100000000002222-10000-1000000000000000000003i−3i3i−3i000000000000
χ5044-2-2-2-2441144-2-2-2-2-2-2-2-2-400-4111100000000002222-10000-100000000000000000000−3i3i−3i3i000000000000
χ514-444-4-41-24-4-121-21-2-12-1204-401-2-1200002i−2i2i−2i00000001-2-12000002i−2i2i−2i0000−ii−ii000000000000−ii−ii0000
χ524-444-4-41-24-4-121-21-2-12-1204-401-2-120000−2i2i−2i2i00000001-2-1200000−2i2i−2i2i0000i−ii−i000000000000i−ii−i0000
χ534-444-4-41-24-4-121-21-2-12-120-4401-2-1200002i−2i−2i2i0000000-121-2000002i−2i−2i2i0000−iii−i000000000000−iii−i0000
χ544-444-4-41-24-4-121-21-2-12-120-4401-2-120000−2i2i2i−2i0000000-121-200000−2i2i2i−2i0000i−i−ii000000000000i−i−ii0000
χ554-444-4-4-214-42-1-21-212-12-104-40-212-12i−2i2i−2i00000000000-212-102i−2i2i−2i0000−ii−ii000000000000−ii−ii00000000
χ564-444-4-4-214-42-1-21-212-12-104-40-212-1−2i2i−2i2i00000000000-212-10−2i2i−2i2i0000i−ii−i000000000000i−ii−i00000000
χ574-444-4-4-214-42-1-21-212-12-10-440-212-12i−2i−2i2i000000000002-1-2102i−2i−2i2i0000−iii−i000000000000−iii−i00000000
χ584-444-4-4-214-42-1-21-212-12-10-440-212-1−2i2i2i−2i000000000002-1-210−2i2i2i−2i0000i−i−ii000000000000i−i−ii00000000
χ594-44-2-4244-22-4-444-2-2-4-422400-4-2-22200000000004-2-42-200002000000000000000000000000000000000000
χ604-4-242-444-22-4-4-2-24422-4-4400-4-2-2220000000000-242-4-200002000000000000000000000000000000000000
χ614-4-2-222441-1-4-4-2-2-2-22222400-411-1-10000000000-2-22210000-1000000000000000000003i−3i−3i3i000000000000
χ624-4-2-222441-1-4-4-2-2-2-22222400-411-1-10000000000-2-22210000-100000000000000000000−3i3i3i−3i000000000000
χ634-4-2-222441-1-4-4-2-2-2-22222-400411-1-1000000004-422-2-2-1000010000000000000000-2-22211-1-1000000000000
χ644-4-2-222441-1-4-4-2-2-2-22222-400411-1-100000000-4422-2-2-100001000000000000000022-2-2-1-111000000000000
χ65888-48-42-4-4-42-42-4-122-4-120000-12-1200000044000000000000000000-2-2000000-2-200000000000000110000
χ66888-48-42-4-4-42-42-4-122-4-120000-12-12000000-4-4000000000000000000220000002200000000000000-1-10000
χ67888-48-4-42-4-4-42-422-1-422-100002-12-10044000000000000000000-2-2000000-2-2000000000000001100000000
χ68888-48-4-42-4-4-42-422-1-422-100002-12-100-4-4000000000000000000220000002200000000000000-1-100000000
χ6988-48-482-4-4-42-4-122-4-122-40000-12-12000044000000000000000000-2-2000000-2-20000000000000011000000
χ7088-48-482-4-4-42-4-122-4-122-40000-12-120000-4-4000000000000000000220000002200000000000000-1-1000000
χ7188-48-48-42-4-4-422-1-422-1-4200002-12-144000000000000000000-2-2000000-2-200000000000000110000000000
χ7288-48-48-42-4-4-422-1-422-1-4200002-12-1-4-4000000000000000000220000002200000000000000-1-10000000000
χ738-88-4-842-4-44-242-4-12-241-20000-121-20000004i−4i000000000000000000−2i2i000000−2i2i00000000000000i−i0000
χ748-88-4-842-4-44-242-4-12-241-20000-121-2000000−4i4i0000000000000000002i−2i0000002i−2i00000000000000−ii0000
χ758-88-4-84-42-444-2-422-14-2-2100002-1-21004i−4i000000000000000000−2i2i000000−2i2i00000000000000i−i00000000
χ768-88-4-84-42-444-2-422-14-2-2100002-1-2100−4i4i0000000000000000002i−2i0000002i−2i00000000000000−ii00000000
χ778-8-484-82-4-44-24-122-41-2-240000-121-200004i−4i000000000000000000−2i2i000000−2i2i00000000000000i−i000000
χ788-8-484-82-4-44-24-122-41-2-240000-121-20000−4i4i0000000000000000002i−2i0000002i−2i00000000000000−ii000000
χ798-8-484-8-42-444-22-1-42-214-200002-1-214i−4i000000000000000000−2i2i000000−2i2i00000000000000i−i0000000000
χ808-8-484-8-42-444-22-1-42-214-200002-1-21−4i4i0000000000000000002i−2i0000002i−2i00000000000000−ii0000000000
χ811616-8-8-8-84-8444-8-24-24-24-2400001-21-200000000000000000000000000000000000000000000000000000000
χ821616-8-8-8-8-8444-844-24-24-24-20000-21-2100000000000000000000000000000000000000000000000000000000
χ8316-16-8-8884-84-4-48-24-242-42-400001-2-1200000000000000000000000000000000000000000000000000000000
χ8416-16-8-888-844-48-44-24-2-42-420000-212-100000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).