Finite Group Databasebeta

← Group #13140913

Character table — Group #13140913

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order122234466644121233666666121236661212121212121212444412121212121212121212121222444488881212121212122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111-1-11111111111-1-11111111-1-1-1-1111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-11111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ71111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-1
χ81111111111-1-11111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-111
χ911-1-111-1-11-11-11-111-1-11-11-11-11-1-111-1-111-1-11i−ii−iii−i−i1-11-111-1-11-1i−ii−i1-1i−ii−iii−i−iii−i−i11-1-11-1i−i
χ1011-1-111-1-11-11-11-111-1-11-11-11-11-1-111-1-111-1-11i−ii−iii−i−i1-11-111-1-1-11i−i−ii-11−iii−iii−i−i−i−iii-1-111-11−ii
χ1111-1-111-1-11-11-11-111-1-11-11-11-11-1-111-1-111-1-11−ii−ii−i−iii1-11-111-1-11-1−ii−ii1-1−ii−ii−i−iii−i−iii11-1-11-1−ii
χ1211-1-111-1-11-11-11-111-1-11-11-11-11-1-111-1-111-1-11−ii−ii−i−iii1-11-111-1-1-11−iii−i-11i−i−ii−i−iiiii−i−i-1-111-11i−i
χ1311-1-111-1-11-1-111-111-1-11-11-1-111-1-111-1-1-1-1111i−ii−iii−i−i-111-1-1-1111-1−iii−i-11−iii−i−i−iii−i−iii-1-1111-1i−i
χ1411-1-111-1-11-1-111-111-1-11-11-1-111-1-111-1-1-1-1111i−ii−iii−i−i-111-1-1-111-11−ii−ii1-1i−ii−i−i−iiiii−i−i11-1-1-11−ii
χ1511-1-111-1-11-1-111-111-1-11-11-1-111-1-111-1-1-1-1111−ii−ii−i−iii-111-1-1-1111-1i−i−ii-11i−i−iiii−i−iii−i−i-1-1111-1−ii
χ1611-1-111-1-11-1-111-111-1-11-11-1-111-1-111-1-1-1-1111−ii−ii−i−iii-111-1-1-111-11i−ii−i1-1−ii−iiii−i−i−i−iii11-1-1-11i−i
χ17222222222222222-1-1-122-1222-1-1-1-122-12222-100000000-1-1-1-1-1-1-1-122000022000000000000-1-1-1-1-1-100
χ18222222222222222-1-1-122-1222-1-1-1-122-12222-100000000-1-1-1-1-1-1-1-1-2-20000-2-200000000000011111100
χ1922222222222222-1222-1-12-122-1-1-1-1-1-12-1-1-1-122222-1-1-1-122-1-1-1-1-1-10022000000-1-1-1-1-1-1000000000000
χ2022222222222222-1222-1-12-122-1-1-1-1-1-12-1-1-1-12-2-2-2-2111122-1-1-1-1-1-100-2-2000000111111000000000000
χ212222222222-2-2222-1-1-122-12-2-2-1-1-1-122-1-2-2-2-2-10000000011-1-11111220000-2-20000000000001111-1-100
χ222222222222-2-2222-1-1-122-12-2-2-1-1-1-122-1-2-2-2-2-10000000011-1-11111-2-2000022000000000000-1-1-1-11100
χ232222222222-2-222-1222-1-12-1-2-2-1-1-1-1-1-12111122222-1-1-1-1-2-2-1-1111100-2-2000000-1-11111000000000000
χ242222222222-2-222-1222-1-12-1-2-2-1-1-1-1-1-1211112-2-2-2-21111-2-2-1-11111002200000011-1-1-1-1000000000000
χ2522222-2-222200-2-222222222002222-2-2-20000-222-2-2222200-2-200000000000000-2-20000000000000000
χ2622222-2-222200-2-222222222002222-2-2-20000-2-2-222-2-2-2-200-2-200000000000000220000000000000000
χ2722222-2-222200-2-2-1222-1-12-100-1-1-1-111-2−i3i3−i3i3-222-2-2-1-1-1-10011−i3i3−i3i3000000000011−i3i3−i3i3000000000000
χ2822222-2-222200-2-2-1222-1-12-100-1-1-1-111-2−i3i3−i3i3-2-2-22211110011−i3i3−i3i30000000000-1-1i3−i3i3−i3000000000000
χ2922222-2-222200-2-2-1222-1-12-100-1-1-1-111-2i3−i3i3−i3-222-2-2-1-1-1-10011i3−i3i3−i3000000000011i3−i3i3−i3000000000000
χ3022222-2-222200-2-2-1222-1-12-100-1-1-1-111-2i3−i3i3−i3-2-2-22211110011i3−i3i3−i30000000000-1-1−i3i3−i3i3000000000000
χ3122-2-222-2-22-22-22-22-1112-2-1-22-2-111-12-2122-2-2-100000000-11-11-1-1112-200002-2000000000000-1-111-1100
χ3222-2-222-2-22-22-22-22-1112-2-1-22-2-111-12-2122-2-2-100000000-11-11-1-111-220000-2200000000000011-1-11-100
χ3322-2-222-2-22-22-22-2-12-2-2-11212-2-111-1-11-2-1-11122i−2i2i−2i−i−iii2-2-11-1-111002i−2i000000−ii−i−iii000000000000
χ3422-2-222-2-22-22-22-2-12-2-2-11212-2-111-1-11-2-1-1112−2i2i−2i2iii−i−i2-2-11-1-11100−2i2i000000i−iii−i−i000000000000
χ3522-2-222-2-22-2-222-22-1112-2-1-2-22-111-12-21-2-222-1000000001-1-1111-1-12-20000-2200000000000011-1-1-1100
χ3622-2-222-2-22-2-222-22-1112-2-1-2-22-111-12-21-2-222-1000000001-1-1111-1-1-2200002-2000000000000-1-1111-100
χ3722-2-222-2-22-2-222-2-12-2-2-1121-22-111-1-11-211-1-122i−2i2i−2i−i−iii-22-1111-1-100−2i2i000000−iiii−i−i000000000000
χ3822-2-222-2-22-2-222-2-12-2-2-1121-22-111-1-11-211-1-12−2i2i−2i2iii−i−i-22-1111-1-1002i−2i000000i−i−i−iii000000000000
χ3922-2-22-22-22-200-2222-2-22-22-2002-2-22-2220000-22i−2i−2i2i2i2i−2i−2i00-2200000000000000−2i2i0000000000000000
χ4022-2-22-22-22-200-2222-2-22-22-2002-2-22-2220000-2−2i2i2i−2i−2i−2i2i2i00-22000000000000002i−2i0000000000000000
χ4122-2-22-22-22-200-22-12-2-2-112100-111-11-12−i3i3i3−i3-22i−2i−2i2i−i−iii001-1−i3i3i3−i30000000000i−i3−3−33000000000000
χ4222-2-22-22-22-200-22-12-2-2-112100-111-11-12−i3i3i3−i3-2−2i2i2i−2iii−i−i001-1−i3i3i3−i30000000000−ii−333−3000000000000
χ4322-2-22-22-22-200-22-12-2-2-112100-111-11-12i3−i3−i3i3-22i−2i−2i2i−i−iii001-1i3−i3−i3i30000000000i−i−333−3000000000000
χ4422-2-22-22-22-200-22-12-2-2-112100-111-11-12i3−i3−i3i3-2−2i2i2i−2iii−i−i001-1i3−i3−i3i30000000000−ii3−3−33000000000000
χ4544444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41111-2-2-22222-2000000002211-1-1-1-10000000000000000000000000000
χ4744444-4-444400-4-44-2-2-244-2400-2-2-2-2-4-420000200000000002200000000000000000000000000000000
χ4844444-4-444400-4-4-2-2-2-2-2-2-2-2001111222−2i32i3−2i32i320000000000-1-1i3−i3i3−i30000000000000000000000000000
χ4944444-4-444400-4-4-2-2-2-2-2-2-2-20011112222i3−2i32i3−2i320000000000-1-1−i3i3−i3i30000000000000000000000000000
χ5044-4-444-4-44-44-44-4-2-222-22-224-41-1-11-222-2-222-200000000-221-111-1-10000000000000000000000000000
χ5144-4-444-4-44-4-444-4-2-222-22-22-441-1-11-22222-2-2-2000000002-21-1-1-1110000000000000000000000000000
χ5244-4-44-44-44-400-444-2224-4-2-400-222-2-44-20000200000000002-200000000000000000000000000000000
χ5344-4-44-44-44-400-44-2-222-22-22001-1-112-2-2−2i32i32i3−2i320000000000-11i3−i3−i3i30000000000000000000000000000
χ5444-4-44-44-44-400-44-2-222-22-22001-1-112-2-22i3−2i3−2i32i320000000000-11−i3i3i3−i30000000000000000000000000000
χ554-44-44004-4-40000444-4-44-4-40044-4-40000000000000000000000000000000000000000000000000000
χ564-44-44004-4-400004-2-22-442-400-2-222000000000000000000000000000000000000000000006−66−60000
χ574-44-44004-4-400004-2-22-442-400-2-22200000000000000000000000000000000000000000000−66−660000
χ584-44-44004-4-40000-244-42-2-4200-2-222000000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ594-44-44004-4-40000-244-42-2-4200-2-2220000000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ604-4-44400-4-44000044-44-4-4-44004-44-40000000000000000000000000000000000000000000000000000
χ614-4-44400-4-4400004-22-2-4-42400-22-22000000000000000000000000000000000000000000006−6−660000
χ624-4-44400-4-4400004-22-2-4-42400-22-2200000000000000000000000000000000000000000000−666−60000
χ634-4-44400-4-440000-24-4422-4-200-22-2200000000000023−23−2323000000000000000000000000000000000000
χ644-4-44400-4-440000-24-4422-4-200-22-22000000000000−232323−23000000000000000000000000000000000000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000000000220022000000-1-1-1-1000000-1-1
χ666666-366-3-3-366-3-300000000-3-300000000000000000000000000000000-2-200-2-2000000111100000011
χ676666-366-3-3-3-6-6-3-30000000033000000000000000000000000000000002200-2-20000001111000000-1-1
χ686666-366-3-3-3-6-6-3-3000000003300000000000000000000000000000000-2-20022000000-1-1-1-100000011
χ6966-6-6-36-63-336-6-3300000000-33000000000000000000000000000000002i−2i002i−2i000000−i−iii000000−ii
χ7066-6-6-36-63-336-6-3300000000-3300000000000000000000000000000000−2i2i00−2i2i000000ii−i−i000000i−i
χ7166-6-6-36-63-33-66-33000000003-3000000000000000000000000000000002i−2i00−2i2i000000ii−i−i000000−ii
χ7266-6-6-36-63-33-66-33000000003-300000000000000000000000000000000−2i2i002i−2i000000−i−iii000000i−i
χ738-88-88008-8-80000-4-4-444-4440022-2-20000000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-4-44-4444-4002-22-20000000000000000000000000000000000000000000000000000
χ7512121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212-12-600-6660000000000000000000000000000000000000000000000000000000000i6−i6i6−i600000000
χ7812-1212-12-600-6660000000000000000000000000000000000000000000000000000000000−i6i6−i6i600000000
χ7912-12-1212-60066-600000000000000000000000000000000000000000000000000000000006−6−6600000000
χ8012-12-1212-60066-60000000000000000000000000000000000000000000000000000000000−666−600000000

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