Finite Group Databasebeta

← Group #13166089

Character table — Group #13166089

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444466888812121212161616161616161616161616161616161818242436363636363636363636363672727272727272727272108
order1222336666663666443666121212123333666666666666441212888824242424242424244412121212121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ3111111111111111111111111111111111111111111-1-11111-1-11111-1-1-1-11-111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-11-1-111-1-1-1-1-1
χ5222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000000-1-1-1-12
χ6222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000001111-2
χ722222-12-12-12-1-1-1-1-12222222-12-12-1-1-1222-1-1-1-1-1-1-1-1-100-1-100220000-1-1-1-10200-1-100000
χ822222-12-12-12-1-1-1-1-12222222-12-12-1-1-1222-1-1-1-1-1-1-1-1-100-1-100-2-2000011110-2001100000
χ92222-12-12-12-12-1-1-1-1222222-12-12-12-1-1-1-1-1222-1-1-1-1-1-100-1-12200-1-1-1-1000020-1-10000000
χ102222-12-12-12-12-1-1-1-1222222-12-12-12-1-1-1-1-1222-1-1-1-1-1-100-1-1-2-20011110000-20110000000
χ1122-2-222-2-222-2-22-2-222-222-2-222-2-222222-2-22-2-222-2-2-2-2002-200000000000000000000000
χ1222-2-222-2-222-2-22-2-222-2-1-11122-2-2-1-1-1-1-111-111-1-11111002-200000000000000000033−3−30
χ1322-2-222-2-222-2-22-2-222-2-1-11122-2-2-1-1-1-1-111-111-1-11111002-2000000000000000000−3−3330
χ1422-2-22-1-212-1-21-111-12-222-2-22-1-212-1-1-12-2-2-111-1-1111100-110000000033−3−300003−300000
χ1522-2-22-1-212-1-21-111-12-222-2-22-1-212-1-1-12-2-2-111-1-1111100-1100000000−3−3330000−3300000
χ1622-2-2-121-2-121-2-111-12-222-2-2-121-2-12-1-1-1112-2-2-1-1111100-11000033−3−30000003−30000000
χ1722-2-2-121-2-121-2-111-12-222-2-2-121-2-12-1-1-1112-2-2-1-1111100-110000−3−333000000−330000000
χ182-22-22222-2-2-2-222-2-200-111-10000-1-1-1-111-111-11111-1-12-2002−22−22−22−22−22−20000001-11-10
χ192-22-22222-2-2-2-222-2-200-111-10000-1-1-1-111-111-11111-1-12-200−22−22−22−22−22−220000001-11-10
χ202-22-22222-2-2-2-222-2-200-111-10000-1-1-1-111-111-11111-1-1-22002−2−222−22−2−22−22000000-11-110
χ212-22-22222-2-2-2-222-2-200-111-10000-1-1-1-111-111-11111-1-1-2200−222−2−22−222−22−2000000-11-110
χ223333333333333333-1-10000-1-1-1-1000000000000000033-1-1111111111111-1-1-1-1-1-10000-1
χ233333333333333333-1-10000-1-1-1-1000000000000000033-1-1-1-1-1-1-1-1-1-1-1-1-1-11111110000-1
χ243333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-111-1-11111-1-1-1-1-11-1-11100001
χ253333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-1-1-111-1-1-1-111111-111-1-100001
χ2644444-24-24-24-2-2-2-2-244-2-2-2-24-24-2-2111-2-2-211111111100-2-200000000000000000000000
χ274444-24-24-24-24-2-2-2-244-2-2-2-2-24-241-211111-2-2-211111100-2-200000000000000000000000
χ284444-2-2-2-2-2-2-2-21111444444-2-2-2-2-2-211-2-2-2-2-2-2111111001100000000000000000000000
χ294444-2-2-2-2-2-2-2-2111144-2-2-2-2-2-2-2-211−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32001100000000000000000000000
χ304444-2-2-2-2-2-2-2-2111144-2-2-2-2-2-2-2-211−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32001100000000000000000000000
χ3144-4-44-2-424-2-42-222-24-4-2-2224-2-42-2111-2221-1-111-1-1-1-100-2200000000000000000000000
χ3244-4-4-242-4-242-4-222-24-4-2-222-242-41-2111-1-1-22211-1-1-1-100-2200000000000000000000000
χ3344-4-4-2-222-2-2221-1-114-444-4-4-2-222-2-211-222-22211-1-1-1-1001-100000000000000000000000
χ3444-4-4-2-222-2-2221-1-114-4-2-222-2-22211−1−3i32−1+3i321-1-11-1-1−1−3i32−1+3i321+3i321−3i321+3i321−3i32001-100000000000000000000000
χ3544-4-4-2-222-2-2221-1-114-4-2-222-2-22211−1+3i32−1−3i321-1-11-1-1−1+3i32−1−3i321−3i321+3i321−3i321+3i32001-100000000000000000000000
χ364-44-44444-4-4-4-444-4-4001-1-1100001111-1-11-1-11-1-1-1-1114-400000000000000000000-11-110
χ374-44-44444-4-4-4-444-4-4001-1-1100001111-1-11-1-11-1-1-1-111-44000000000000000000001-11-10
χ384-44-44-24-2-42-42-2-22200-222-20000-211122-2-1-11-1-1-1-11100000022−220000−22−2200000000000
χ394-44-44-24-2-42-42-2-22200-222-20000-211122-2-1-11-1-1-1-111000000−222200002−22−200000000000
χ404-44-4-24-242-42-4-2-22200-222-200001-211-1-1122-2-1-1-1-111000022−2200−22−22000000000000000
χ414-44-4-24-242-42-4-2-22200-222-200001-211-1-1122-2-1-1-1-1110000−2222002−22−2000000000000000
χ424-4-4444-4-4-4-4444-44-4001-11-100001111-11-1-11-1-1-111-1-100000000000000000000003−3−330
χ434-4-4444-4-4-4-4444-44-4001-11-100001111-11-1-11-1-1-111-1-10000000000000000000000−333−30
χ444-4-4444-4-4-4-4444-44-400-22-220000-2-2-2-22-222-2222-2-222000000000000000000000000000
χ454-4-444-2-42-424-2-22-2200-22-220000-21112-22-11-1-1-111-1-10000000000006−6−6600000000000
χ464-4-444-2-42-424-2-22-2200-22-220000-21112-22-11-1-1-111-1-1000000000000−666−600000000000
χ474-4-44-242-42-4-24-22-2200-22-2200001-211-11-12-22-1-111-1-1000000006−6−66000000000000000
χ484-4-44-242-42-4-24-22-2200-22-2200001-211-11-12-22-1-111-1-100000000−666−6000000000000000
χ4966666-36-36-36-3-3-3-3-3-2-20000-21-210000000000000000001100220000-1-1-1-10-2001100000
χ5066666-36-36-36-3-3-3-3-3-2-20000-21-210000000000000000001100-2-2000011110200-1-100000
χ516666-36-36-36-36-3-3-3-3-2-200001-21-2000000000000000000112200-1-1-1-10000-20110000000
χ526666-36-36-36-36-3-3-3-3-2-200001-21-200000000000000000011-2-2001111000020-1-10000000
χ5366-6-666-6-666-6-66-6-66-220000-2-222000000000000000000-2200000000000000000000000
χ5466-6-66-3-636-3-63-333-3-220000-212-10000000000000000001-10000000033−3−30000−3300000
χ5566-6-66-3-636-3-63-333-3-220000-212-10000000000000000001-100000000−3−33300003−300000
χ5666-6-6-363-6-363-6-333-3-2200001-2-120000000000000000001-1000033−3−3000000−330000000
χ5766-6-6-363-6-363-6-333-3-2200001-2-120000000000000000001-10000−3−3330000003−30000000
χ588-88-88-48-4-84-84-4-444002-2-2200002-1-1-1-2-2211-11111-1-1000000000000000000000000000
χ598-88-8-48-484-84-8-4-444002-2-220000-12-1-111-1-2-221111-1-1000000000000000000000000000
χ608-88-8-4-4-4-4444422-2-2002-2-220000-1-11−3i321+3i3211-111-1−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i32000000000000000000000000000
χ618-88-8-4-4-4-4444422-2-2002-2-220000-1-11+3i321−3i3211-111-1−1−3i32−1+3i32−1−3i32−1+3i321+3i321−3i32000000000000000000000000000
χ628-88-8-4-4-4-4444422-2-200-444-4000022-1-1-2-22-2-221111-1-1000000000000000000000000000
χ638-8-888-4-84-848-4-44-44002-22-200002-1-1-1-22-21-1111-1-111000000000000000000000000000
χ648-8-88-484-84-8-48-44-44002-22-20000-12-1-11-11-22-211-1-111000000000000000000000000000
χ658-8-88-4-44444-4-42-22-2002-22-20000-1-11−3i321+3i321-111-11−1+3i32−1−3i321−3i321+3i32−1+3i32−1−3i32000000000000000000000000000
χ668-8-88-4-44444-4-42-22-2002-22-20000-1-11+3i321−3i321-111-11−1−3i32−1+3i321+3i321−3i32−1−3i32−1+3i32000000000000000000000000000
χ678-8-88-4-44444-4-42-22-200-44-44000022-1-1-22-2-22-211-1-111000000000000000000000000000
χ6812121212-6-6-6-6-6-6-6-63333-4-400002222000000000000000000-1-100000000000000000000000
χ691212-12-12-6-666-6-6663-3-33-44000022-2-2000000000000000000-1100000000000000000000000

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