Finite Group Databasebeta

← Group #13149615

Character table — Group #13149615

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order1222344666441212336666661212366612121212121212122222224444121212121212121212121212222444466666666121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-11-11-11-111-1-1-1-1-1-111-1-1-1-11-11-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-11-11-1-1-1-1-1-111-1-1-1-111-11-11
χ51111111111-1-11111111111-1-11111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-11111-1-1-1-11111-1-1-11-11
χ61111111111-1-11111111111-1-11111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-11-11-1-11-1-111-1-111-1-111111-11-1
χ71111111111-1-11111111111-1-11111-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-11-1-1-1-11111-1-1111111-1-111-1-1-1-1
χ81111111111-1-11111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11-111-1-11111111-1-1-1-1-1-111-111-1
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111-1-1-111111111-1-1-1-11-1-11
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-11111111111111-111-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1
χ1311111-1-1111-11-1-111111111-111111-1-1-1-1-1-111111111-1-1111111-11-1-1-1-111-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1
χ1411111-1-1111-11-1-111111111-111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-11-1-1-1-111-1-1-11111-1-111-1-1-1-111-1-111-1-111
χ1511111-1-1111-11-1-111111111-111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-11-1-1-1-11111-1-11-1111-1-111-1-1-1-111111-1-11
χ1611111-1-1111-11-1-111111111-111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-1111-111-11-1-1-1-1-111111111-1-1-111-1
χ17222222222222222-12-12-12-122-1-1-1-12222-1-12200002200000000-1-1-1-1-1-1-1-10020202000000-1-10000-1-10-10-1
χ18222222222222222-12-12-12-122-1-1-1-12222-1-1220000-2-200000000-1-1-1-1-1-1-1-100-20-20-2000000110000110101
χ1922222222222222-12-12-12-1222-1-1-1-1-1-1-1-122-1-12200002222-1-1-1-122-1-1-1-1-1-1200000000-1-1-1-10000-1-1000000
χ2022222222222222-12-12-12-1222-1-1-1-1-1-1-1-122-1-1-2-20000-2-2-2-2111122-1-1-1-1-1-1-2000000001111000011000000
χ212222222222-2-2222-12-12-12-1-2-2-1-1-1-1-2-222-1-1-2-2000022000000001111-1-11100-20-202000000-1-10000-1-10101
χ222222222222-2-2222-12-12-12-1-2-2-1-1-1-1-2-222-1-1-2-20000-2-2000000001111-1-111002020-2000000110000110-10-1
χ232222222222-2-222-12-12-12-12-2-2-1-1-1-111-1-1221122000022-2-21111-2-211-1-111-200000000-1-1110000-1-1000000
χ242222222222-2-222-12-12-12-12-2-2-1-1-1-111-1-12211-2-20000-2-222-1-1-1-1-2-211-1-11120000000011-1-1000011000000
χ2522222-2-22222-2-2-22-12-12-12-12-2-1-1-1-122-2-211-2-200002200000000-11-1-1111100-2020-2000000-1-1000011010-1
χ2622222-2-22222-2-2-22-12-12-12-12-2-1-1-1-122-2-211-2-20000-2-200000000-11-1-111110020-202000000110000-1-10-101
χ2722222-2-22222-2-2-2-12-12-12-122-2-1-1-1-1-1-111-2-211220000-2-2-2-211112-2-1-11111200000000-1-1-1-1000011000000
χ2822222-2-22222-2-2-2-12-12-12-122-2-1-1-1-1-1-111-2-211-2-200002222-1-1-1-12-2-1-11111-20000000011110000-1-1000000
χ2922222-2-2222-22-2-22-12-12-12-1-22-1-1-1-1-2-2-2-21122000022000000001-11111-1-10020-20-2000000-1-10000110-101
χ3022222-2-2222-22-2-22-12-12-12-1-22-1-1-1-1-2-2-2-211220000-2-2000000001-11111-1-100-20202000000110000-1-1010-1
χ3122222-2-2222-22-2-2-12-12-12-12-22-1-1-1-11111-2-2-1-1220000-2-222-1-1-1-1-221111-1-1-200000000-1-111000011000000
χ3222222-2-2222-22-2-2-12-12-12-12-22-1-1-1-11111-2-2-1-1-2-2000022-2-21111-221111-1-120000000011-1-10000-1-1000000
χ3322-2-222i−2i2-2-2002i−2i2222-2-2-2-2002-22-2002i−2i2i−2i002-200002i−2i00000000002i−2i000000000002-20000002i−2i000000
χ3422-2-222i−2i2-2-2002i−2i2222-2-2-2-2002-22-2002i−2i2i−2i00-220000−2i2i00000000002i−2i00000000000-22000000−2i2i000000
χ3522-2-222i−2i2-2-2002i−2i-12-121-21-200-11-11−i3i3−ii2i−2i3−32-200002i−2i0033−3−300−i3i3−ii3−3000000000-11−i3i30000−ii000000
χ3622-2-222i−2i2-2-2002i−2i-12-121-21-200-11-11−i3i3−ii2i−2i3−3-220000−2i2i00−3−33300−i3i3−ii3−30000000001-1i3−i30000i−i000000
χ3722-2-222i−2i2-2-2002i−2i-12-121-21-200-11-11i3−i3−ii2i−2i−332-200002i−2i00−3−33300i3−i3−ii−33000000000-11i3−i30000−ii000000
χ3822-2-222i−2i2-2-2002i−2i-12-121-21-200-11-11i3−i3−ii2i−2i−33-220000−2i2i0033−3−300i3−i3−ii−330000000001-1−i3i30000i−i000000
χ3922-2-22−2i2i2-2-200−2i2i2222-2-2-2-2002-22-200−2i2i−2i2i002-20000−2i2i0000000000−2i2i000000000002-2000000−2i2i000000
χ4022-2-22−2i2i2-2-200−2i2i2222-2-2-2-2002-22-200−2i2i−2i2i00-2200002i−2i0000000000−2i2i00000000000-220000002i−2i000000
χ4122-2-22−2i2i2-2-200−2i2i-12-121-21-200-11-11−i3i3i−i−2i2i−332-20000−2i2i00−3−33300−i3i3i−i−33000000000-11−i3i30000i−i000000
χ4222-2-22−2i2i2-2-200−2i2i-12-121-21-200-11-11−i3i3i−i−2i2i−33-2200002i−2i0033−3−300−i3i3i−i−330000000001-1i3−i30000−ii000000
χ4322-2-22−2i2i2-2-200−2i2i-12-121-21-200-11-11i3−i3i−i−2i2i3−32-20000−2i2i0033−3−300i3−i3i−i3−3000000000-11i3−i30000i−i000000
χ4422-2-22−2i2i2-2-200−2i2i-12-121-21-200-11-11i3−i3i−i−2i2i3−3-2200002i−2i00−3−33300i3−i3i−i3−30000000001-1−i3i30000−ii000000
χ452-2-22200-2-22000022-2-2-2-222002-2-2200000000002-22-2002-22-22-20000000000000002-200002-20000000000
χ462-2-22200-2-22000022-2-2-2-222002-2-2200000000002-2-2200-22-22-220000000000000002-20000-220000000000
χ472-2-22200-2-22000022-2-2-2-222002-2-220000000000-222-200-22-22-22000000000000000-2200002-20000000000
χ482-2-22200-2-22000022-2-2-2-222002-2-220000000000-22-22002-22-22-2000000000000000-220000-220000000000
χ4944444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000000000-2-21111110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-4111122-2-2-2-2220000000000000022-1-111-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41111-2-222222200000000000000-2211-1-1-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-441111222222-2-2000000000000002-2-1-1-1-1110000000000000000000000000
χ5344-4-444i−4i4-4-4004i−4i4-24-2-42-4200-22-22004i−4i−2i2i00000000000000000000−2i2i000000000000000000000000000
χ5444-4-444i−4i4-4-4004i−4i-2-2-2-22222001-11-1−2i32i3−2i2i−2i2i23−230000000000000000i3−i3i−i−330000000000000000000000000
χ5544-4-444i−4i4-4-4004i−4i-2-2-2-22222001-11-12i3−2i3−2i2i−2i2i−23230000000000000000−i3i3i−i3−30000000000000000000000000
χ5644-4-44−4i4i4-4-400−4i4i4-24-2-42-4200-22-2200−4i4i2i−2i000000000000000000002i−2i000000000000000000000000000
χ5744-4-44−4i4i4-4-400−4i4i-2-2-2-22222001-11-1−2i32i32i−2i2i−2i−23230000000000000000i3−i3−ii3−30000000000000000000000000
χ5844-4-44−4i4i4-4-400−4i4i-2-2-2-22222001-11-12i3−2i32i−2i2i−2i23−230000000000000000−i3i3−ii−330000000000000000000000000
χ594-44-4400-44-4000044-4-444-4-40044-4-40000000000000000000000000000000000000000000000000000000
χ604-44-4400-44-400004-2-424-2-4200-2-222000000000000000000000000000000000000000000000000023−230000
χ614-44-4400-44-400004-2-424-2-4200-2-2220000000000000000000000000000000000000000000000000−23230000
χ624-44-4400-44-40000-242-4-242-400-2-22200000000000000000023−23−2323000000000000000000000000000000000
χ634-44-4400-44-40000-242-4-242-400-2-222000000000000000000−232323−23000000000000000000000000000000000
χ644-4-44400-4-4400004-2-42-424-200-222-20000000000004-400000000000000000000000000000-220000000000
χ654-4-44400-4-4400004-2-42-424-200-222-2000000000000-44000000000000000000000000000002-20000000000
χ664-4-44400-4-440000-242-42-4-2400-222-200000000000000004-4-22-22000000000000000000000000000000000
χ674-4-44400-4-440000-242-42-4-2400-222-20000000000000000-442-22-2000000000000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-300000000000000220000000000000000000202020-1-1000000-1-10000-10-10
χ696666-366-3-3-366-3-300000000-3-300000000000000-2-20000000000000000000-20-20-20110000001100001010
χ706666-366-3-3-3-6-6-3-3000000003300000000000000220000000000000000000-20-2020-1-1000000-1-100001010
χ716666-366-3-3-3-6-6-3-3000000003300000000000000-2-200000000000000000002020-2011000000110000-10-10
χ726666-3-6-6-3-3-36-63300000000-3300000000000000220000000000000000000-2020-20-1-100000011000010-10
χ736666-3-6-6-3-3-36-63300000000-3300000000000000-2-2000000000000000000020-202011000000-1-10000-1010
χ746666-3-6-6-3-3-3-6633000000003-30000000000000022000000000000000000020-20-20-1-1000000110000-1010
χ756666-3-6-6-3-3-3-6633000000003-300000000000000-2-20000000000000000000-20202011000000-1-1000010-10
χ768-88-8800-88-80000-4-444-4-4440022-2-20000000000000000000000000000000000000000000000000000000
χ778-8-88800-8-880000-4-44444-4-4002-2-220000000000000000000000000000000000000000000000000000000
χ781212-12-12-612i−12i-66600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ791212-12-12-6−12i12i-666006i−6i000000000000000000000000000000000000000000000000000000000000000000000
χ8012-1212-12-6006-6600000000000000000000000000000000000000000000000000000000000000023−2300000000
χ8112-1212-12-6006-66000000000000000000000000000000000000000000000000000000000000000−232300000000
χ8212-12-1212-60066-600000000000000000000000000004-40000000000000000000000000-220000000000000000
χ8312-12-1212-60066-60000000000000000000000000000-4400000000000000000000000002-20000000000000000

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