Finite Group Databasebeta

← Group #72220756

Character table — Group #72220756

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222444444668888888888889999121212121212121212121616181818181818181824242424242424243636363636363636363636363636545454545454727272728181108108108108108108
order1233663336662233333366666622226666666666364444666666666666666666121212121212121222444412121212226612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111-1-1111111111111111-1-1111111111111-1-111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111-1-11111111111111-1-111111111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-111
χ5111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ7111111111111-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-111
χ8111111111111-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1-11111-1-1
χ91-111-1-1111-1-1-11-1111111-1-1-1-1-1-111-1-111-1-111-1-11-11-1i−ii−i11-1-11111-1-1-1-11-11-11-1i−ii−ii−ii−i1-1i−ii−ii−ii−i1-11-1i−ii−i
χ101-111-1-1111-1-1-11-1111111-1-1-1-1-1-111-1-111-1-111-1-11-11-1−ii−ii11-1-11111-1-1-1-11-11-11-1−ii−ii−ii−ii1-1−ii−ii−ii−ii1-11-1−ii−ii
χ111-111-1-1111-1-1-11-1111111-1-1-1-1-1-11-11-111-1-111-1-11-11-1i−i−ii11-1-11111-1-1-1-1-111-1-11i−i−iii−i−ii-11i−i−iii−i−ii-11-11i−i−ii
χ121-111-1-1111-1-1-11-1111111-1-1-1-1-1-11-11-111-1-111-1-11-11-1−iii−i11-1-11111-1-1-1-1-111-1-11−iii−i−iii−i-11−iii−i−iii−i-11-11−iii−i
χ131-111-1-1111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-111-1-111-111-1i−ii−i11-1-1-1-1-1-111111-11-11-1i−ii−ii−ii−i-11−ii−iii−ii−i1-1-11−ii−ii
χ141-111-1-1111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-111-1-111-111-1−ii−ii11-1-1-1-1-1-111111-11-11-1−ii−ii−ii−ii-11i−ii−i−ii−ii1-1-11i−ii−i
χ151-111-1-1111-1-1-1-11111111-1-1-1-1-1-11-11-1-1-111-1-111-111-1i−i−ii11-1-1-1-1-1-11111-111-1-11i−i−iii−i−ii1-1−iii−ii−i−ii-111-1−iii−i
χ161-111-1-1111-1-1-1-11111111-1-1-1-1-1-11-11-1-1-111-1-111-111-1−iii−i11-1-1-1-1-1-11111-111-1-11−iii−i−iii−i1-1i−i−ii−iii−i-111-1i−i−ii
χ1722222222222200222222222222-222-20000000000220000-2-2-2-20000000022-2-222000000000000000000-2-2000000
χ1822222222222200222222222222-2-2-2-20000000000220000-2-2-2-200000000-2-2-2-2-2-200000000000000000022000000
χ19222-12-12-12-122222-12-1-1-12-1-1-12-120022-12-1-1-1-1-122-1-100222-12-12-1-1-12-1-1-100-1-10000-1-1002200002200-1-1000000-1-1
χ20222-12-12-12-122222-12-1-1-12-1-1-12-120022-12-1-1-1-1-122-1-100-2-22-12-12-1-1-12-1-1-100-1-100001100-2-20000-2-2001100000011
χ21222-12-12-12-122-2-22-12-1-1-12-1-1-12-12002-21-211111-2-2-1-100222-12-1-2111-211100-1-10000-1-100220000-2-200-1-100000011
χ22222-12-12-12-122-2-22-12-1-1-12-1-1-12-12002-21-211111-2-2-1-100-2-22-12-1-2111-211100-1-100001100-2-20000220011000000-1-1
χ2322-12-122-12-12222-12-12-1-1-12-1-1-122002-12-12-1-1-1-122-1-12200-12-12-12-1-1-12-1-100-1-100-1-1002200002200-1-1000000-1-100
χ2422-12-122-12-12222-12-12-1-1-12-1-1-122002-12-12-1-1-1-122-1-1-2-200-12-12-12-1-1-12-1-100-1-1001100-2-20000-2-200110000001100
χ2522-12-122-12-122-2-2-12-12-1-1-12-1-1-1220021-21-21111-2-2-1-12200-12-121-2111-21100-1-100-1-100220000-2-200-1-10000001100
χ2622-12-122-12-122-2-2-12-12-1-1-12-1-1-1220021-21-21111-2-2-1-1-2-200-12-121-2111-21100-1-1001100-2-20000220011000000-1-100
χ272-222-2-2222-2-2-200222222-2-2-2-2-2-2-22-2200000000002-20000-2-222000000002-2-222-2000000000000000000-22000000
χ282-222-2-2222-2-2-200222222-2-2-2-2-2-2-2-22200000000002-20000-2-22200000000-22-22-220000000000000000002-2000000
χ292-22-1-212-121-2-22-22-12-1-1-1-2111-21200-22-1-21-1-1112-2-11002i−2i2-1-212-1-1-1-211100-110000−ii002i−2i00002i−2i00−ii000000−ii
χ302-22-1-212-121-2-22-22-12-1-1-1-2111-21200-22-1-21-1-1112-2-1100−2i2i2-1-212-1-1-1-211100-110000i−i00−2i2i0000−2i2i00i−i000000i−i
χ312-22-1-212-121-2-2-222-12-1-1-1-2111-21200-2-212-111-1-1-22-11002i−2i2-1-21-21112-1-1-100-110000−ii002i−2i0000−2i2i00−ii000000i−i
χ322-22-1-212-121-2-2-222-12-1-1-1-2111-21200-2-212-111-1-1-22-1100−2i2i2-1-21-21112-1-1-100-110000i−i00−2i2i00002i−2i00i−i000000−ii
χ332-2-121-22-121-2-22-2-12-12-1-11-2111-2200-2-121-2-1-1112-2-112i−2i00-121-2-12-1-11-21100-1100−ii002i−2i00002i−2i00−ii000000−ii00
χ342-2-121-22-121-2-22-2-12-12-1-11-2111-2200-2-121-2-1-1112-2-11−2i2i00-121-2-12-1-11-21100-1100i−i00−2i2i0000−2i2i00i−i000000i−i00
χ352-2-121-22-121-2-2-22-12-12-1-11-2111-2200-21-2-1211-1-1-22-112i−2i00-121-21-211-12-1-100-1100−ii002i−2i0000−2i2i00−ii000000i−i00
χ362-2-121-22-121-2-2-22-12-12-1-11-2111-2200-21-2-1211-1-1-22-11−2i2i00-121-21-211-12-1-100-1100i−i00−2i2i00002i−2i00i−i000000−ii00
χ3744444414-24-210011-2-2-2-2-2-2-2-211044000000000001122220000000000001100-2-22222-1-1-1-1000000-1-1-1-100000000
χ3844444414-24-210011-2-2-2-2-2-2-2-2110440000000000011-2-2-2-20000000000001100-2-2-2-2-2-21111000000111100000000
χ3944444414-24-210011-2-2-2-2-2-2-2-2110-4-4000000000001122-2-2000000000000-1-1002222-2-2-1-111000000-1-11100000000
χ4044444414-24-210011-2-2-2-2-2-2-2-2110-4-40000000000011-2-222000000000000-1-10022-2-22211-1-100000011-1-100000000
χ41444444-24141-222-2-211111111-2-2044022222222-1-1-2-200000000-1-1-1-1-1-1-1-1-2-2001100000000220000000000-1-10000
χ42444444-24141-222-2-211111111-2-20-4-4022222222-1-1-2-200000000-1-1-1-1-1-1-1-12200-1-100000000-2-20000000000110000
χ43444444-24141-2-2-2-2-211111111-2-20440-2-2-2-2-2-2-2-211-2-20000000011111111-2-2001100000000-2-20000000000110000
χ44444444-24141-2-2-2-2-211111111-2-20-4-40-2-2-2-2-2-2-2-211-2-200000000111111112200-1-100000000220000000000-1-10000
χ45444-24-24-24-244004-24-2-2-24-2-2-24-2-400-40000000000-2-20000-42-420000000000220000000000000000000000000000
χ4644-24-244-24-24400-24-24-2-2-24-2-2-24-400-40000000000-2-200002-42-40000000000220000000000000000000000000000
χ4744-2-2-2-241414400-2-2-2-211-2-211-2-2-400-400003-33-3001100002222003-3003-300-1-10000000000000000000000000000
χ4844-2-2-2-241414400-2-2-2-211-2-211-2-2-400-40000-33-3300110000222200-3300-3300-1-10000000000000000000000000000
χ4944-2-2-2-241414444-2-2-2-211-2-211-2-24004-2-2-2-2111144110000-2-2-2-2-2-211-2-21100110000000000000000000000000000
χ5044-2-2-2-2414144-4-4-2-2-2-211-2-211-2-240042222-1-1-1-1-4-4110000-2-2-2-222-1-122-1-100110000000000000000000000000000
χ514-444-4-414-2-42-10011-2-2-2-22222-1-104-4000000000001-12i−2i2i−2i0000000000001-100-222i−2i2i−2i−ii−ii000000−ii−ii00000000
χ524-444-4-414-2-42-10011-2-2-2-22222-1-104-4000000000001-1−2i2i−2i2i0000000000001-100-22−2i2i−2i2ii−ii−i000000i−ii−i00000000
χ534-444-4-414-2-42-10011-2-2-2-22222-1-10-44000000000001-12i−2i−2i2i000000000000-11002-22i−2i−2i2i−iii−i000000−iii−i00000000
χ544-444-4-414-2-42-10011-2-2-2-22222-1-10-44000000000001-1−2i2i2i−2i000000000000-11002-2−2i2i2i−2ii−i−ii000000i−i−ii00000000
χ554-444-4-4-241-4-122-2-2-21111-1-1-1-12204-4022-2-222-2-2-11-2200000000-1-1-1-11111-22001-1000000002-20000000000-110000
χ564-444-4-4-241-4-122-2-2-21111-1-1-1-1220-44022-2-222-2-2-11-2200000000-1-1-1-111112-200-1100000000-2200000000001-10000
χ574-444-4-4-241-4-12-22-2-21111-1-1-1-12204-40-2-222-2-2221-1-22000000001111-1-1-1-1-22001-100000000-2200000000001-10000
χ584-444-4-4-241-4-12-22-2-21111-1-1-1-1220-440-2-222-2-2221-1-22000000001111-1-1-1-12-200-11000000002-20000000000-110000
χ594-44-2-424-242-4-4004-24-2-2-2-4222-42-40040000000000-220000-424-200000000002-20000000000000000000000000000
χ604-4-242-44-242-4-400-24-24-2-22-4222-4-40040000000000-2200002-4-2400000000002-20000000000000000000000000000
χ614-4-2-222414-1-4-400-2-2-2-21122-1-122-400400003-3-33001-1000022-2-2003-300-3300-110000000000000000000000000000
χ624-4-2-222414-1-4-400-2-2-2-21122-1-122-40040000-333-3001-1000022-2-200-33003-300-110000000000000000000000000000
χ634-4-2-222414-1-4-44-4-2-2-2-21122-1-122400-4-2-22211-1-14-41-10000-2-222-2-21122-1-1001-10000000000000000000000000000
χ644-4-2-222414-1-4-4-44-2-2-2-21122-1-122400-422-2-2-1-111-441-10000-2-22222-1-1-2-211001-10000000000000000000000000000
χ65888-48-42-4-4-4-42002-1-4222-42222-100000000000000-1-1004400000000000000000000-2-200-2-2000000001100000000
χ66888-48-42-4-4-4-42002-1-4222-42222-100000000000000-1-100-4-40000000000000000000022002200000000-1-100000000
χ67888-48-4-4-42-42-444-422-1-1-12-1-1-1-4200004-24-2-2-2-2-2-2-22200000000-2111-211100000000000000000000000000000000
χ68888-48-4-4-42-42-4-4-4-422-1-1-12-1-1-1-420000-42-4222222222000000002-1-1-12-1-1-100000000000000000000000000000000
χ6988-48-482-4-4-4-4200-122-4222-422-1200000000000000-1-14400000000000000000000-2-200-2-200000000110000000000
χ7088-48-482-4-4-4-4200-122-4222-422-1200000000000000-1-1-4-40000000000000000000022002200000000-1-10000000000
χ7188-48-48-4-42-42-4442-4-12-1-1-12-1-12-40000-24-24-2-2-2-2-2-222000000001-2111-21100000000000000000000000000000000
χ7288-48-48-4-42-42-4-4-42-4-12-1-1-12-1-12-400002-42-42222222200000000-12-1-1-12-1-100000000000000000000000000000000
χ7388-4-4-4-4-42222-44422-1-15-4-1-15-4220000-2-2-2-24-24-2-2-2-1-10000000011-2111-2100000000000000000000000000000000
χ7488-4-4-4-4-42222-44422-1-1-45-1-1-45220000-2-2-2-2-24-24-2-2-1-100000000111-2111-200000000000000000000000000000000
χ7588-4-4-4-4-42222-4-4-422-1-15-4-1-15-42200002222-42-4222-1-100000000-1-12-1-1-12-100000000000000000000000000000000
χ7688-4-4-4-4-42222-4-4-422-1-1-45-1-1-4522000022222-42-422-1-100000000-1-1-12-1-1-1200000000000000000000000000000000
χ778-88-4-842-4-444-2002-1-42224-2-2-2-2100000000000000-11004i−4i00000000000000000000−2i2i00−2i2i00000000i−i00000000
χ788-88-4-842-4-444-2002-1-42224-2-2-2-2100000000000000-1100−4i4i000000000000000000002i−2i002i−2i00000000−ii00000000
χ798-88-4-84-4-424-244-4-422-1-1-1-21114-200004-2-42-2-222-222-200000000-21112-1-1-100000000000000000000000000000000
χ808-88-4-84-4-424-24-44-422-1-1-1-21114-20000-424-222-2-22-22-2000000002-1-1-1-211100000000000000000000000000000000
χ818-8-484-82-4-444-200-122-422-24-2-21-200000000000000-114i−4i00000000000000000000−2i2i00−2i2i00000000i−i0000000000
χ828-8-484-82-4-444-200-122-422-24-2-21-200000000000000-11−4i4i000000000000000000002i−2i002i−2i00000000−ii0000000000
χ838-8-484-8-4-424-244-42-4-12-1-11-211-240000-242-4-2-222-222-2000000001-211-12-1-100000000000000000000000000000000
χ848-8-484-8-4-424-24-442-4-12-1-11-211-2400002-4-2422-2-22-22-200000000-12-1-11-21100000000000000000000000000000000
χ858-8-4-444-422-2-244-422-1-15-411-54-2-20000-2-2224-2-42-22-110000000011-21-1-12-100000000000000000000000000000000
χ868-8-4-444-422-2-244-422-1-1-45114-5-2-20000-2-222-242-4-22-1100000000111-2-1-1-1200000000000000000000000000000000
χ878-8-4-444-422-2-24-4422-1-15-411-54-2-2000022-2-2-424-22-2-1100000000-1-12-111-2100000000000000000000000000000000
χ888-8-4-444-422-2-24-4422-1-1-45114-5-2-2000022-2-22-4-242-2-1100000000-1-1-12111-200000000000000000000000000000000
χ891616-8-8-8-844-84-8400-2-244-2-244-2-2-2-20000000000000011000000000000000000000000000000000000000000000000
χ9016-16-8-88844-8-48-400-2-244-2-2-4-42222000000000000001-1000000000000000000000000000000000000000000000000

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