Finite Group Databasebeta

← Group #13151337

Character table — Group #13151337

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order122234466622121233666666662222366666661212121244444444446666666666121222444466661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111-1-11111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ61111111111-1-11111111111-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111-1-11111111111-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111
χ81111111111-1-11111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-1
χ911111-1-11111-1-1-1111111111-11111111-1-1111-1-1-1-111-1-111-1-1-1-111111-111-1-1-1-11-11-11-111-1-111-1-111-1-1-1-11-11-1
χ1011111-1-11111-1-1-1111111111-11111111-1-1111-1-1-1-1-1-111-1-111-1-111111-111-1-1-1-11-1-11-1111-1-1-1-111-1-111-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1-1-1-1-1111-1-1111-1-1-1-111-1-1-1-11111-1-1-1-11-111-1-1-1-1-111-1-11-1-11111-1-1-1-111111-1-11
χ1211111-1-11111-1-1-1111111111-1-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-1-1-11-111-1-1-1-1-11-111-1-1-111-1-11111-1-111-111-1
χ1311111-1-1111-11-1-111111111-1111111-1-111111-1-1-1-111-1-111-1-1-1-11111-11-1-111-1-1-11-11-11-1-11111-1-111-1-1-1-1-11-11
χ1411111-1-1111-11-1-111111111-1111111-1-111111-1-1-1-1-1-111-1-111-1-11111-11-1-111-1-1-111-11-1-1-111-1-111-1-111-1-11-11-1
χ1511111-1-1111-11-1-111111111-11-1-1-1-11-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-111-1-11-1-111-111-1-111-1-1-1-11111-111-1
χ1611111-1-1111-11-1-111111111-11-1-1-1-11-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-111-1-11-11-1-1111-1-1-1-11111-1-1111-1-11
χ17222222222222222-1-1-122-12222222-1-1-1-1-1-1-1-1-1-1220000000022-1-1-1-122-1-1-1-1-1-1220000-1-1-1-100000000-1-10000
χ18222222222222222-1-1-122-1222-2-2-2-2-1-1-1-1-1-1-1-1-1-12200000000-2-2111122-1-1-1-1-1-1-2-20000111100000000110000
χ1922222222222222-1222-1-12-1220000-12222-1-1-122-1-100002222000000-1-1-1-1-1-1-1-100002200000000-1-1-1-10000-1-1
χ2022222222222222-1222-1-12-1220000-12222-1-1-122-1-10000-2-2-2-2000000-1-1-1-1-1-1-1-10000-2-2000000001111000011
χ212222222222-2-2222-1-1-122-12-2-22222-11111-1-1-1-1-1220000000022-1-1-1-1-2-21111-1-1-2-20000111100000000-1-10000
χ222222222222-2-2222-1-1-122-12-2-2-2-2-2-2-11111-1-1-1-1-12200000000-2-21111-2-21111-1-1220000-1-1-1-100000000110000
χ232222222222-2-222-1222-1-12-1-2-20000-1-2-2-2-2-1-1-122-1-100002222000000111111-1-10000-2-200000000-1-1-1-1000011
χ242222222222-2-222-1222-1-12-1-2-20000-1-2-2-2-2-1-1-122-1-10000-2-2-2-2000000111111-1-10000220000000011110000-1-1
χ2522222-2-22222-2-2-22-1-1-122-122-22222-1-1-111-1-1-111-2-200000000-2-2-1-1-1-12-2-1-111112-20000-1-11100000000110000
χ2622222-2-22222-2-2-22-1-1-122-122-2-2-2-2-2-1-1-111-1-1-111-2-2000000002211112-2-1-11111-22000011-1-100000000-1-10000
χ2722222-2-22222-2-2-2-1222-1-12-12-20000-122-2-2-1-1-1-2-211000022-2-2000000-11-1-1111100002-200000000-1-1110000-11
χ2822222-2-22222-2-2-2-1222-1-12-12-20000-122-2-2-1-1-1-2-2110000-2-222000000-11-1-111110000-220000000011-1-100001-1
χ2922222-2-2222-22-2-22-1-1-122-12-222222-111-1-1-1-1-111-2-200000000-2-2-1-1-1-1-2211-1-111-22000011-1-100000000110000
χ3022222-2-2222-22-2-22-1-1-122-12-22-2-2-2-2-111-1-1-1-1-111-2-200000000221111-2211-1-1112-20000-1-11100000000-1-10000
χ3122222-2-2222-22-2-2-1222-1-12-1-220000-1-2-222-1-1-1-2-211000022-2-20000001-111-1-1110000-2200000000-1-11100001-1
χ3222222-2-2222-22-2-2-1222-1-12-1-220000-1-2-222-1-1-1-2-2110000-2-2220000001-111-1-11100002-20000000011-1-10000-11
χ3322-2-22002-2-20000222-22-2-2-20022-2-2200002-2-20000002i−2i002i−2i0022-2-2000000000000000000002i−2i002i−2i000000
χ3422-2-22002-2-20000222-22-2-2-20022-2-2200002-2-2000000−2i2i00−2i2i0022-2-200000000000000000000−2i2i00−2i2i000000
χ3522-2-22002-2-20000222-22-2-2-200-2-222200002-2-20000002i−2i00−2i2i00-2-222000000000000000000002i−2i00−2i2i000000
χ3622-2-22002-2-20000222-22-2-2-200-2-222200002-2-2000000−2i2i002i−2i00-2-22200000000000000000000−2i2i002i−2i000000
χ372-22-2200-22-2000022-22-22-2-2002-22-220000-22-200002i−2i002i−2i00002-22-20000000000000000002i−2i002i−2i00000000
χ382-22-2200-22-2000022-22-22-2-2002-22-220000-22-20000−2i2i00−2i2i00002-22-2000000000000000000−2i2i00−2i2i00000000
χ392-22-2200-22-2000022-22-22-2-200-22-2220000-22-200002i−2i00−2i2i0000-22-220000000000000000002i−2i00−2i2i00000000
χ402-22-2200-22-2000022-22-22-2-200-22-2220000-22-20000−2i2i002i−2i0000-22-22000000000000000000−2i2i002i−2i00000000
χ412-2-2222-2-2-22002-222-2-2-2-222002-2-2220000-2-222-22-2000000002-22-2-220000002-20000000000000000002-20000
χ422-2-2222-2-2-22002-222-2-2-2-22200-222-220000-2-222-22-200000000-22-222-20000002-2000000000000000000-220000
χ432-2-2222-2-2-22002-22-111-2-2-12002-2-22-1−i3i3−i3i311-1-112-2000000002-2-111-100−i3i3−i3i3-11000000−i3i3−i3i300000000-110000
χ442-2-2222-2-2-22002-22-111-2-2-12002-2-22-1i3−i3i3−i311-1-112-2000000002-2-111-100i3−i3i3−i3-11000000i3−i3i3−i300000000-110000
χ452-2-2222-2-2-22002-22-111-2-2-1200-222-2-1−i3i3−i3i311-1-112-200000000-221-1-1100−i3i3−i3i3-11000000i3−i3i3−i3000000001-10000
χ462-2-2222-2-2-22002-22-111-2-2-1200-222-2-1i3−i3i3−i311-1-112-200000000-221-1-1100i3−i3i3−i3-11000000−i3i3−i3i3000000001-10000
χ472-2-222-22-2-2200-2222-2-2-2-222002-2-2220000-2-22-22-2200000000-222-2-22000000-22000000000000000000-220000
χ482-2-222-22-2-2200-2222-2-2-2-22200-222-220000-2-22-22-22000000002-2-222-2000000-220000000000000000002-20000
χ492-2-222-22-2-2200-222-111-2-2-12002-2-22-1−i3i3i3−i311-11-1-2200000000-22-111-100−i3i3i3−i31-1000000−i3i3i3−i3000000001-10000
χ502-2-222-22-2-2200-222-111-2-2-12002-2-22-1i3−i3−i3i311-11-1-2200000000-22-111-100i3−i3−i3i31-1000000i3−i3−i3i3000000001-10000
χ512-2-222-22-2-2200-222-111-2-2-1200-222-2-1−i3i3i3−i311-11-1-22000000002-21-1-1100−i3i3i3−i31-1000000i3−i3−i3i300000000-110000
χ522-2-222-22-2-2200-222-111-2-2-1200-222-2-1i3−i3−i3i311-11-1-22000000002-21-1-1100i3−i3−i3i31-1000000−i3i3i3−i300000000-110000
χ5344444444444444-2-2-2-2-2-2-2-24400001-2-2-2-2111-2-2-2-200000000000000-2-2111111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-4000012222111-2-2-2-20000000000000022-1-1-1-111000000000000000000000000
χ5544444-4-44444-4-4-4-2-2-2-2-2-2-2-24-400001-2-222111222200000000000000-2211-1-1-1-1000000000000000000000000
χ5644444-4-4444-44-4-4-2-2-2-2-2-2-2-2-440000122-2-21112222000000000000002-2-1-111-1-1000000000000000000000000
χ5744-4-44004-4-400004-2-224-42-40044-4-4-20000-22200000000000000-2-22200000000000000000000000000000000
χ5844-4-44004-4-400004-2-224-42-400-4-444-20000-2220000000000000022-2-200000000000000000000000000000000
χ5944-4-44004-4-40000-244-4-22-42000000-20000-22200000000004i−4i000000000000000000000000000000−2i2i000000
χ6044-4-44004-4-40000-244-4-22-42000000-20000-2220000000000−4i4i0000000000000000000000000000002i−2i000000
χ614-44-4400-44-400004-22-2-442-4004-44-4-200002-2200000000000000-22-2200000000000000000000000000000000
χ624-44-4400-44-400004-22-2-442-400-44-44-200002-22000000000000002-22-200000000000000000000000000000000
χ634-44-4400-44-40000-24-442-2-42000000-200002-22000000004i−4i000000000000000000000000000000−2i2i00000000
χ644-44-4400-44-40000-24-442-2-42000000-200002-2200000000−4i4i0000000000000000000000000000002i−2i00000000
χ654-4-4444-4-4-44004-4-24-4-4224-2000000-2000022-24-4-2200000000000000000000-22000000000000000000000000
χ664-4-4444-4-4-44004-4-2-22222-2-20000001−2i32i3−2i32i3-1-11-22-220000000000000000i3−i3i3−i31-1000000000000000000000000
χ674-4-4444-4-4-44004-4-2-22222-2-200000012i3−2i32i3−2i3-1-11-22-220000000000000000−i3i3−i3i31-1000000000000000000000000
χ684-4-444-44-4-4400-44-24-4-4224-2000000-2000022-2-442-2000000000000000000002-2000000000000000000000000
χ694-4-444-44-4-4400-44-2-22222-2-20000001−2i32i32i3−2i3-1-112-22-20000000000000000i3−i3−i3i3-11000000000000000000000000
χ704-4-444-44-4-4400-44-2-22222-2-200000012i3−2i3−2i32i3-1-112-22-20000000000000000−i3i3i3−i3-11000000000000000000000000
χ716666-366-3-3-366-3-300000000-3-3000000000000000022220000000000000000000022000000-1-1-1-1000000-1-100
χ726666-366-3-3-366-3-300000000-3-30000000000000000-2-2-2-200000000000000000000-2-200000011110000001100
χ736666-366-3-3-3-6-6-3-300000000330000000000000000222200000000000000000000-2-2000000-1-1-1-10000001100
χ746666-366-3-3-3-6-6-3-300000000330000000000000000-2-2-2-200000000000000000000220000001111000000-1-100
χ756666-3-6-6-3-3-36-63300000000-33000000000000000022-2-2000000000000000000002-2000000-1-111000000-1100
χ766666-3-6-6-3-3-36-63300000000-330000000000000000-2-22200000000000000000000-2200000011-1-10000001-100
χ776666-3-6-6-3-3-3-6633000000003-3000000000000000022-2-200000000000000000000-22000000-1-1110000001-100
χ786666-3-6-6-3-3-3-6633000000003-30000000000000000-2-222000000000000000000002-200000011-1-1000000-1100
χ7988-8-88008-8-80000-4-4-44-4444000000200002-2-200000000000000000000000000000000000000000000000000
χ808-88-8800-88-80000-4-44-44-44400000020000-22-200000000000000000000000000000000000000000000000000
χ811212-12-12-600-666000000000000000000000000000000004i−4i000000000000000000000000000000−2i2i0000000000
χ821212-12-12-600-66600000000000000000000000000000000−4i4i0000000000000000000000000000002i−2i0000000000
χ8312-1212-12-6006-660000000000000000000000000000004i−4i000000000000000000000000000000−2i2i000000000000
χ8412-1212-12-6006-66000000000000000000000000000000−4i4i0000000000000000000000000000002i−2i000000000000
χ8512-12-1212-612-1266-600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-6-121266-6006-6000000000000000000000000000000000000000000000000000000000000000000000000

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