Finite Group Databasebeta

← Group #13151338

Character table — Group #13151338

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order122234466622121233666666663666666612121212224412121212666666121244444444446612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111-1-11111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ61111111111-1-11111111111-1-11-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-111
χ81111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1
χ911111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-111-1-1-1-1-1-11-111-1-1-1-11-11-11-11-11-11111-1-111-1-111-1-11-11-1
χ1011111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-111-1-1-1-1-1-11-111-1-1-1-1-11-111-1-11-1111-1-111-1-11111-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-11111111-111-1-1-1-11-1-11-111-1-11-1-111-1-1-1-111-1-1111-1-11
χ1211111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-11111111-111-1-1-1-1-111-1-11-111-1-1-1-1-11111-1-1-1-111-111-1
χ1311111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-1-1-1-11-1-111-1-11-11-1-11-11-111111-1-111-1-1-1-111-11-11
χ1411111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-1-1-1-11-1-111-1-1-11-11-111-11-111-1-111-1-111-1-1111-11-1
χ1511111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-1111111-11-1-111-1-11-1-111-1-111-1-1-111-1-1-1-11111-1-1-111-1
χ1611111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-1111111-11-1-111-1-1-111-11-11-1-11-1-1-1-11111-1-111-1-11-1-11
χ17222222222222222-1-1-1222-122-1-1-1-1-1-1-1-122-1-12222-1-1-1-122-1-1-1-1-1-10000220000-1-100000000-1-1-1-10000
χ18222222222222222-1-1-1222-122-1-1-1-1-1-1-1-122-1-1-2-2-2-2111122-1-1-1-1-1-10000-2-20000110000000011110000
χ1922222222222222-1222-1-1-1222-12222-1-1-1-1-12200000000-1-1-1-1-1-1-1-10022000022000000-1-1-1-1000000-1-1
χ2022222222222222-1222-1-1-1222-12222-1-1-1-1-12200000000-1-1-1-1-1-1-1-100-2-20000-2-2000000111100000011
χ212222222222-2-2222-1-1-1222-1-2-2-11111-1-1-122-1-12222-1-1-1-1-2-21111-1-10000-2-20000-1-10000000011110000
χ222222222222-2-2222-1-1-1222-1-2-2-11111-1-1-122-1-1-2-2-2-21111-2-21111-1-100002200001100000000-1-1-1-10000
χ232222222222-2-222-1222-1-1-12-2-2-1-2-2-2-2-1-1-1-1-12200000000111111-1-100220000-2-2000000-1-1-1-100000011
χ242222222222-2-222-1222-1-1-12-2-2-1-2-2-2-2-1-1-1-1-12200000000111111-1-100-2-20000220000001111000000-1-1
χ2522222-2-22222-2-2-22-1-1-1222-12-2-1-1-111-1-1-1-2-21122-2-211112-2-1-1111100002-20000-1-100000000-1-1110000
χ2622222-2-22222-2-2-22-1-1-1222-12-2-1-1-111-1-1-1-2-211-2-222-1-1-1-12-2-1-111110000-220000110000000011-1-10000
χ2722222-2-22222-2-2-2-1222-1-1-122-2-122-2-2-1-1-111-2-200000000-11-1-11111002-200002-2000000-1-111000000-11
χ2822222-2-22222-2-2-2-1222-1-1-122-2-122-2-2-1-1-111-2-200000000-11-1-1111100-220000-2200000011-1-10000001-1
χ2922222-2-2222-22-2-22-1-1-1222-1-22-111-1-1-1-1-1-2-21122-2-21111-2211-1-1110000-220000-1-10000000011-1-10000
χ3022222-2-2222-22-2-22-1-1-1222-1-22-111-1-1-1-1-1-2-211-2-222-1-1-1-1-2211-1-11100002-200001100000000-1-1110000
χ3122222-2-2222-22-2-2-1222-1-1-12-22-1-2-222-1-1-111-2-2000000001-111-1-111002-20000-22000000-1-1110000001-1
χ3222222-2-2222-22-2-2-1222-1-1-12-22-1-2-222-1-1-111-2-2000000001-111-1-11100-2200002-200000011-1-1000000-11
χ332-2-2222-2-2-22002-222-2-2-2-2220020000-2-222-22-22-22-222-2-20000002-200000000002-20000000000000000
χ342-2-2222-2-2-22002-222-2-2-2-2220020000-2-222-22-2-22-22-2-2220000002-20000000000-220000000000000000
χ352-2-2222-2-2-22002-22-111-2-22-100-1−i3i3−i3i311-12-2-112-22-2-1-11100−i3i3−i3i3-110000000000-1100000000−i3i3−i3i30000
χ362-2-2222-2-2-22002-22-111-2-22-100-1−i3i3−i3i311-12-2-11-22-2211-1-100−i3i3−i3i3-1100000000001-100000000i3−i3i3−i30000
χ372-2-2222-2-2-22002-22-111-2-22-100-1i3−i3i3−i311-12-2-112-22-2-1-11100i3−i3i3−i3-110000000000-1100000000i3−i3i3−i30000
χ382-2-2222-2-2-22002-22-111-2-22-100-1i3−i3i3−i311-12-2-11-22-2211-1-100i3−i3i3−i3-1100000000001-100000000−i3i3−i3i30000
χ392-2-222-22-2-2200-2222-2-2-2-2220020000-2-22-22-222-2-22-2-222000000-2200000000002-20000000000000000
χ402-2-222-22-2-2200-2222-2-2-2-2220020000-2-22-22-22-222-222-2-2000000-220000000000-220000000000000000
χ412-2-222-22-2-2200-222-111-2-22-100-1−i3i3i3−i311-1-221-12-2-2211-1-100−i3i3i3−i31-10000000000-1100000000−i3i3i3−i30000
χ422-2-222-22-2-2200-222-111-2-22-100-1−i3i3i3−i311-1-221-1-222-2-1-11100−i3i3i3−i31-100000000001-100000000i3−i3−i3i30000
χ432-2-222-22-2-2200-222-111-2-22-100-1i3−i3−i3i311-1-221-12-2-2211-1-100i3−i3−i3i31-10000000000-1100000000i3−i3−i3i30000
χ442-2-222-22-2-2200-222-111-2-22-100-1i3−i3−i3i311-1-221-1-222-2-1-11100i3−i3−i3i31-100000000001-100000000−i3i3i3−i30000
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111-2-2-2-200000000-2-21111110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-412222111-2-2-2-20000000022-1-1-1-1110000000000000000000000000000
χ4744444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-222111222200000000-2211-1-1-1-10000000000000000000000000000
χ4844444-4-4444-44-4-4-2-2-2-2-2-2-2-2-44122-2-21112222000000002-2-1-111-1-10000000000000000000000000000
χ4944-4-44004-4-40000444-44-4-4-400400004-4-4000000000000000000000000000000000000000000000000
χ5044-4-44004-4-400004-2-224-4-4200-20000-2220000000023−2323−23000000000000000000000000000000000000
χ5144-4-44004-4-400004-2-224-4-4200-20000-22200000000−2323−2323000000000000000000000000000000000000
χ5244-4-44004-4-40000-244-4-222-400-20000-22200000000000000000000000000000000000023−230000000000
χ5344-4-44004-4-40000-244-4-222-400-20000-222000000000000000000000000000000000000−23230000000000
χ544-44-4400-44-4000044-44-44-4-40040000-44-4000000000000000000000000000000000000000000000000
χ554-44-4400-44-400004-22-2-44-4200-200002-220000000023−23−2323000000000000000000000000000000000000
χ564-44-4400-44-400004-22-2-44-4200-200002-2200000000−232323−23000000000000000000000000000000000000
χ574-44-4400-44-40000-24-442-22-400-200002-220000000000000000000000000000000000000023−2300000000
χ584-44-4400-44-40000-24-442-22-400-200002-2200000000000000000000000000000000000000−232300000000
χ594-4-4444-4-4-44004-4-24-4-422-2400-2000022-2-224-400000000000000-220000000000000000000000000000
χ604-4-4444-4-4-44004-4-2-22222-2-2001−2i32i3−2i32i3-1-11-22-220000000000i3−i3i3−i31-10000000000000000000000000000
χ614-4-4444-4-4-44004-4-2-22222-2-20012i3−2i32i3−2i3-1-11-22-220000000000−i3i3−i3i31-10000000000000000000000000000
χ624-4-444-44-4-4400-44-24-4-422-2400-2000022-22-2-44000000000000002-20000000000000000000000000000
χ634-4-444-44-4-4400-44-2-22222-2-2001−2i32i32i3−2i3-1-112-22-20000000000i3−i3−i3i3-110000000000000000000000000000
χ644-4-444-44-4-4400-44-2-22222-2-20012i3−2i3−2i32i3-1-112-22-20000000000−i3i3i3−i3-110000000000000000000000000000
χ656666-366-3-3-366-3-300000000-3-30000000000000000000000000000220000220000-1-1-1-100000000-1-100
χ666666-366-3-3-366-3-300000000-3-30000000000000000000000000000-2-20000-2-200001111000000001100
χ676666-366-3-3-3-6-6-3-300000000330000000000000000000000000000220000-2-20000-1-1-1-1000000001100
χ686666-366-3-3-3-6-6-3-300000000330000000000000000000000000000-2-20000220000111100000000-1-100
χ696666-3-6-6-3-3-36-63300000000-3300000000000000000000000000002-200002-20000-1-11100000000-1100
χ706666-3-6-6-3-3-36-63300000000-330000000000000000000000000000-220000-22000011-1-1000000001-100
χ716666-3-6-6-3-3-3-6633000000003-300000000000000000000000000002-20000-220000-1-111000000001-100
χ726666-3-6-6-3-3-3-6633000000003-30000000000000000000000000000-2200002-2000011-1-100000000-1100
χ7388-8-88008-8-80000-4-4-44-444400200002-2-2000000000000000000000000000000000000000000000000
χ748-88-8800-88-80000-4-44-44-4440020000-22-2000000000000000000000000000000000000000000000000
χ751212-12-12-600-6660000000000000000000000000000000000000000000000000000000023−23000000000000
χ761212-12-12-600-66600000000000000000000000000000000000000000000000000000000−2323000000000000
χ7712-1212-12-6006-6600000000000000000000000000000000000000000000000000000023−2300000000000000
χ7812-1212-12-6006-66000000000000000000000000000000000000000000000000000000−232300000000000000
χ7912-12-1212-612-1266-600-66000000000000000000000000000000000000000000000000000000000000000000
χ8012-12-1212-6-121266-6006-6000000000000000000000000000000000000000000000000000000000000000000

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