Finite Group Databasebeta

← Group #13166093

Character table — Group #13166093

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444466888812121212161616161616161616161616161616161818242436363636363636363636363672727272727272727272108
order122233666666366644366612121212333366666666666622121288882424242424242424446666121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ3111111111111111111111111111111111111111111-1-11111-1-11111-1-1-1-11-1-1-1-1-111-1-1-1
χ4111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-11-1-1-1-1-1-111-1
χ5222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000-1-1-1-100002
χ6222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000011110000-2
χ722222-122-1-1-12-1-1-1-1222222-12-122-1-1-1222-1-1-1-1-1-1-1-1-100-1-12200-1-1-1-10000200000-1-1000
χ822222-122-1-1-12-1-1-1-1222222-12-122-1-1-1222-1-1-1-1-1-1-1-1-100-1-1-2-20011110000-20000011000
χ92222-12-1-1222-1-1-1-1-12222222-12-1-12-1-1-1-1-1222-1-1-1-1-1-100-1-100220000-1-1-1-102000000-1-10
χ102222-12-1-1222-1-1-1-1-12222222-12-1-12-1-1-1-1-1222-1-1-1-1-1-100-1-100-2-2000011110-2000000110
χ1122-2-2222-22-2-2-222-2-200-111-10000-1-1-1-111-111-11111-1-12-2002−22−222−2−222−2−20011-1-100000
χ1222-2-2222-22-2-2-222-2-200-111-10000-1-1-1-111-111-11111-1-12-200−22−22−2−222−2−2220011-1-100000
χ1322-2-2222-22-2-2-222-2-200-111-10000-1-1-1-111-111-11111-1-1-22002−2−2222−2−2−2−22200-1-11100000
χ1422-2-2222-22-2-2-222-2-200-111-10000-1-1-1-111-111-11111-1-1-2200−222−2−2−22222−2−200-1-11100000
χ152-2-2222-2-2-22-222-2-222-222-2-22-2-2222222-2-22-2-222-2-2-2-2002-200000000000000000000000
χ162-2-2222-2-2-22-222-2-222-2-1-1112-2-22-1-1-1-1-111-111-1-11111002-200000000000000−i3i3−i3i300000
χ172-2-2222-2-2-22-222-2-222-2-1-1112-2-22-1-1-1-1-111-111-1-11111002-200000000000000i3−i3i3−i300000
χ182-2-222-1-2-21-112-111-12-222-2-2-1-2122-1-1-12-2-2-111-1-1111100-1100003−33−300000000003−3000
χ192-2-222-1-2-21-112-111-12-222-2-2-1-2122-1-1-12-2-2-111-1-1111100-110000−33−330000000000−33000
χ202-2-22-1211-22-2-1-111-12-222-2-221-2-1-12-1-1-1112-2-2-1-1111100-1100000000−i3i3−i3i300000000−i3i30
χ212-2-22-1211-22-2-1-111-12-222-2-221-2-1-12-1-1-1112-2-2-1-1111100-1100000000i3−i3i3−i300000000i3−i30
χ223333333333333333-1-10000-1-1-1-1000000000000000033-1-1111111111111-1-10000-1-1-1-1-1
χ233333333333333333-1-10000-1-1-1-1000000000000000033-1-1-1-1-1-1-1-1-1-1-1-1-1-11100001111-1
χ243333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-111-1-11111-1-1-1-1-110000-1-1111
χ253333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-1-1-111-1-1-1-111111-1000011-1-11
χ2644444-244-2-2-24-2-2-2-244-2-2-2-2-24-24-2111-2-2-211111111100-2-200000000000000000000000
χ274444-24-2-2444-2-2-2-2-244-2-2-2-24-24-21-211111-2-2-211111100-2-200000000000000000000000
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
χ3144-4-4444-44-4-4-444-4-4001-1-1100001111-1-11-1-11-1-1-1-1114-40000000000000000-1-11100000
χ3244-4-4444-44-4-4-444-4-4001-1-1100001111-1-11-1-11-1-1-1-111-44000000000000000011-1-100000
χ3344-4-44-24-4-222-4-2-22200-222-20000-211122-2-1-11-1-1-1-111000022−2200−2−222000000000000000
χ3444-4-44-24-4-222-4-2-22200-222-20000-211122-2-1-11-1-1-1-1110000−22220022−2−2000000000000000
χ3544-4-4-24-224-4-42-2-22200-222-200001-211-1-1122-2-1-1-1-11100000022−220000−2−22200000000000
χ3644-4-4-24-224-4-42-2-22200-222-200001-211-1-1122-2-1-1-1-111000000−2222000022−2−200000000000
χ374-44-444-44-4-44-44-44-4001-11-100001111-11-1-11-1-1-111-1-1000000000000000000−i3i3i3−i300000
χ384-44-444-44-4-44-44-44-4001-11-100001111-11-1-11-1-1-111-1-1000000000000000000i3−i3−i3i300000
χ394-44-444-44-4-44-44-44-400-22-220000-2-2-2-22-222-2222-2-222000000000000000000000000000
χ404-44-44-2-4422-2-4-22-2200-22-220000-21112-22-11-1-1-111-1-1000000006−6−66000000000000000
χ414-44-44-2-4422-2-4-22-2200-22-220000-21112-22-11-1-1-111-1-100000000−666−6000000000000000
χ424-44-4-242-2-4-442-22-2200-22-2200001-211-11-12-22-1-111-1-1000000000000i6−i6−i6i600000000000
χ434-44-4-242-2-4-442-22-2200-22-2200001-211-11-12-22-1-111-1-1000000000000−i6i6i6−i600000000000
χ444-4-444-2-4-42-224-222-24-4-2-222-2-424-2111-2221-1-111-1-1-1-100-2200000000000000000000000
χ454-4-44-2422-44-4-2-222-24-4-2-22242-4-21-2111-1-1-22211-1-1-1-100-2200000000000000000000000
χ464-4-44-2-2222-22-21-1-114-444-4-4-222-2-2-211-222-22211-1-1-1-1001-100000000000000000000000
χ474-4-44-2-2222-22-21-1-114-4-2-222-222-211−1−3i32−1+3i321-1-11-1-1−1−3i32−1+3i321+3i321−3i321+3i321−3i32001-100000000000000000000000
χ484-4-44-2-2222-22-21-1-114-4-2-222-222-211−1+3i32−1−3i321-1-11-1-1−1+3i32−1−3i321−3i321+3i321−3i321+3i32001-100000000000000000000000
χ4966666-366-3-3-36-3-3-3-3-2-200001-21-2000000000000000000112200-1-1-1-10000-20000011000
χ5066666-366-3-3-36-3-3-3-3-2-200001-21-200000000000000000011-2-20011110000200000-1-1000
χ516666-36-3-3666-3-3-3-3-3-2-20000-21-210000000000000000001100220000-1-1-1-10-2000000110
χ526666-36-3-3666-3-3-3-3-3-2-20000-21-210000000000000000001100-2-20000111102000000-1-10
χ536-6-6666-6-6-66-666-6-66-220000-222-2000000000000000000-2200000000000000000000000
χ546-6-666-3-6-63-336-333-3-22000012-1-20000000000000000001-100003−33−30000000000−33000
χ556-6-666-3-6-63-336-333-3-22000012-1-20000000000000000001-10000−33−3300000000003−3000
χ566-6-66-3633-66-6-3-333-3-220000-2-1210000000000000000001-100000000−i3i3−i3i300000000i3−i30
χ576-6-66-3633-66-6-3-333-3-220000-2-1210000000000000000001-100000000i3−i3i3−i300000000−i3i30
χ5888-8-88-48-8-444-8-4-444002-2-2200002-1-1-1-2-2211-11111-1-1000000000000000000000000000
χ5988-8-8-48-448-8-84-4-444002-2-220000-12-1-111-1-2-221111-1-1000000000000000000000000000
χ6088-8-8-4-4-44-444422-2-2002-2-220000-1-11−3i321+3i3211-111-1−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i32000000000000000000000000000
χ6188-8-8-4-4-44-444422-2-2002-2-220000-1-11+3i321−3i3211-111-1−1−3i32−1+3i32−1−3i32−1+3i321+3i321−3i32000000000000000000000000000
χ6288-8-8-4-4-44-444422-2-200-444-4000022-1-1-2-22-2-221111-1-1000000000000000000000000000
χ638-88-88-4-8844-4-8-44-44002-22-200002-1-1-1-22-21-1111-1-111000000000000000000000000000
χ648-88-8-484-4-8-884-44-44002-22-20000-12-1-11-11-22-211-1-111000000000000000000000000000
χ658-88-8-4-44-444-442-22-2002-22-20000-1-11−3i321+3i321-111-11−1+3i32−1−3i321−3i321+3i32−1+3i32−1−3i32000000000000000000000000000
χ668-88-8-4-44-444-442-22-2002-22-20000-1-11+3i321−3i321-111-11−1−3i32−1+3i321+3i321−3i32−1−3i32−1+3i32000000000000000000000000000
χ678-88-8-4-44-444-442-22-200-44-44000022-1-1-22-2-22-211-1-111000000000000000000000000000
χ6812121212-6-6-6-6-6-6-6-63333-4-400002222000000000000000000-1-100000000000000000000000
χ6912-12-1212-6-6666-66-63-3-33-4400002-2-22000000000000000000-1100000000000000000000000

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