Finite Group Databasebeta

← Group #13149504

Character table — Group #13149504

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order1222344666441212336666661212366612121212121212122244444444121212121212121212121212244444466661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ51111111111-1-11111111111-1-11111-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-11-1-111111111-1-1-1-111-1-1-1-1
χ61111111111-1-11111111111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-1-11111-1-1-1-1-1-111111111-1-1
χ71111111111-1-11111111111-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-111
χ81111111111-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11-111-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111111111-1-111111-1-1-111-1-1-1-11-1-11-111-1-111-1-111-1-1-1-11-11-1
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-1-1-111-1-11-11-11-111111-1-111-1-111-1-1-111-1
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1-1-111-1-111-11-11-1-1-11111-1-1-1-111111-1-11
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-111-1-1-11-111-11-1-1-1-1-1-11111-1-111-11-11
χ1311111-1-1111-11-1-111111111-111111-1-111-1-1-1-1111111-1-1111111-11-1-1-1-111-1-1-11-1-1111-1-111-1-1-1-111-1-1-11-11
χ1411111-1-1111-11-1-111111111-111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11-1-1-1-1111-1-1111-11111-1-11111-1-1-1-11-1-11
χ1511111-1-1111-11-1-111111111-111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11-1-1-1-111111-1-1-11-1-11111-1-111-1-111-111-1
χ1611111-1-1111-11-1-111111111-111111-1-111-1-1-1-1-1-1-1-111-1-1111111-11-1-1-1-111-111-111-1-1-1-1-1-1-111-1-111111-11-1
χ17222222222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1220000222222-1-1-1-122-1-1-1-1-1-1200000000-1-10000-1-1-1-1000000
χ18222222222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1220000-2-2-2-2-2-2111122-1-1-1-1-1-1-2000000001100001111000000
χ1922222222222222-12-1-1222-122-1-1-1-1222222-1-122000000000000-1-1-1-1-1-1-1-10222000-1-10000000000-1-100-1-1
χ2022222222222222-12-1-1222-122-1-1-1-1222222-1-1-2-2000000000000-1-1-1-1-1-1-1-10-2-2-2000110000000000110011
χ212222222222-2-2222-122-1-1-12-2-2-1-1-1-11111-1-122000022-2-2-2-2-1-1-1-1-2-2-1-11111200000000-1-100001111000000
χ222222222222-2-2222-122-1-1-12-2-2-1-1-1-11111-1-1220000-2-222221111-2-2-1-11111-200000000110000-1-1-1-1000000
χ232222222222-2-222-12-1-1222-1-2-2-1-1-1-1-2-2-2-222-1-12200000000000011-1-1111102-2-2000-1-10000000000-1-10011
χ242222222222-2-222-12-1-1222-1-2-2-1-1-1-1-2-2-2-222-1-1-2-200000000000011-1-111110-2220001100000000001100-1-1
χ2522222-2-22222-2-2-22-122-1-1-122-2-1-1-1-1-1-11111-2-200002222-2-2-1-1-1-12-211-1-111-200000000110000-1-111000000
χ2622222-2-22222-2-2-22-122-1-1-122-2-1-1-1-1-1-11111-2-20000-2-2-2-22211112-211-1-111200000000-1-1000011-1-1000000
χ2722222-2-22222-2-2-2-12-1-1222-12-2-1-1-1-122-2-2-2-21122000000000000-1111-1-1110-22-2000-1-100000000001100-11
χ2822222-2-22222-2-2-2-12-1-1222-12-2-1-1-1-122-2-2-2-211-2-2000000000000-1111-1-11102-22000110000000000-1-1001-1
χ2922222-2-2222-22-2-22-122-1-1-12-22-1-1-1-111-1-111-2-2000022-2-222-1-1-1-1-221111-1-1-20000000011000011-1-1000000
χ3022222-2-2222-22-2-22-122-1-1-12-22-1-1-1-111-1-111-2-20000-2-222-2-21111-221111-1-1200000000-1-10000-1-111000000
χ3122222-2-2222-22-2-2-12-1-1222-1-22-1-1-1-1-2-222-2-211220000000000001-11111-1-10-2-22000-1-1000000000011001-1
χ3222222-2-2222-22-2-2-12-1-1222-1-22-1-1-1-1-2-222-2-211-2-20000000000001-11111-1-1022-2000110000000000-1-100-11
χ332-22-222-22-2-2002-222-2-2-22-22002-22-200002-22-20000002i−2i2i−2i0000002-200000000000000000002i−2i2i−2i000000
χ342-22-222-22-2-2002-222-2-2-22-22002-22-200002-22-2000000−2i2i−2i2i0000002-20000000000000000000−2i2i−2i2i000000
χ352-22-222-22-2-2002-22-1-2-21-11200-11-113−33−3-112-20000002i−2i2i−2i−i3−i3i3i300-113−33−3000000000−i3i30000−ii−ii000000
χ362-22-222-22-2-2002-22-1-2-21-11200-11-113−33−3-112-2000000−2i2i−2i2ii3i3−i3−i300-113−33−3000000000i3−i30000i−ii−i000000
χ372-22-222-22-2-2002-22-1-2-21-11200-11-11−33−33-112-20000002i−2i2i−2ii3i3−i3−i300-11−33−33000000000i3−i30000−ii−ii000000
χ382-22-222-22-2-2002-22-1-2-21-11200-11-11−33−33-112-2000000−2i2i−2i2i−i3−i3i3i300-11−33−33000000000−i3i30000i−ii−i000000
χ392-22-22-222-2-200-2222-2-2-22-22002-22-20000-22-220000002i−2i−2i2i000000-2200000000000000000002i−2i−2i2i000000
χ402-22-22-222-2-200-2222-2-2-22-22002-22-20000-22-22000000−2i2i2i−2i000000-220000000000000000000−2i2i2i−2i000000
χ412-22-22-222-2-200-222-1-2-21-11200-11-113−3−331-1-220000002i−2i−2i2i−i3−i3i3i3001-13−3−33000000000i3−i30000−iii−i000000
χ422-22-22-222-2-200-222-1-2-21-11200-11-113−3−331-1-22000000−2i2i2i−2ii3i3−i3−i3001-13−3−33000000000−i3i30000i−i−ii000000
χ432-22-22-222-2-200-222-1-2-21-11200-11-11−333−31-1-220000002i−2i−2i2ii3i3−i3−i3001-1−333−3000000000−i3i30000−iii−i000000
χ442-22-22-222-2-200-222-1-2-21-11200-11-11−333−31-1-22000000−2i2i2i−2i−i3−i3i3i3001-1−333−3000000000i3−i30000i−i−ii000000
χ452-2-22200-2-220000222-2-2-22-20022-2-2000000002-22i−2i2i−2i00002i−2i2i−2i0000000000000002-2002i−2i000000000000
χ462-2-22200-2-220000222-2-2-22-20022-2-2000000002-2−2i2i−2i2i0000−2i2i−2i2i0000000000000002-200−2i2i000000000000
χ472-2-22200-2-220000222-2-2-22-20022-2-200000000-222i−2i−2i2i0000−2i2i−2i2i000000000000000-22002i−2i000000000000
χ482-2-22200-2-220000222-2-2-22-20022-2-200000000-22−2i2i2i−2i00002i−2i2i−2i000000000000000-2200−2i2i000000000000
χ4944444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000000000-2-21111110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-411112222-2-2-2-2000000000000002211-1-1-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41111-2-222222200000000000000-22-1-111-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-44111122-2-22222000000000000002-2-1-1-1-1110000000000000000000000000
χ5344-4-4400-44-4000044-444-4-4-4004-4-440000000000000000000000000000000000000000000000000000000
χ5444-4-4400-44-400004-2-44-222-400-222-200000000000000000023−23−2323000000000000000000000000000000000
χ5544-4-4400-44-400004-2-44-222-400-222-2000000000000000000−232323−23000000000000000000000000000000000
χ5644-4-4400-44-40000-242-24-4-4200-222-2000000000000000000000000000000000000000000000000023−230000
χ5744-4-4400-44-40000-242-24-4-4200-222-20000000000000000000000000000000000000000000000000−23230000
χ584-44-444-44-4-4004-4-2422-44-4-200-22-2200004-4-220000000000000000-2200000000000000000000000000000
χ594-44-444-44-4-4004-4-2-2222-22-2001-11-123−2323−23-22-2200000000000000001-1−33−330000000000000000000000000
χ604-44-444-44-4-4004-4-2-2222-22-2001-11-1−2323−2323-22-2200000000000000001-13−33−30000000000000000000000000
χ614-44-44-444-4-400-44-2422-44-4-200-22-220000-442-200000000000000002-200000000000000000000000000000
χ624-44-44-444-4-400-44-2-2222-22-2001-11-123−23−23232-22-20000000000000000-11−333−30000000000000000000000000
χ634-44-44-444-4-400-44-2-2222-22-2001-11-1−232323−232-22-20000000000000000-113−3−330000000000000000000000000
χ644-4-44400-4-4400004-24-422-2-400-2-2220000000000004i−4i0000−2i2i−2i2i000000000000000000000000000000000
χ654-4-44400-4-4400004-24-422-2-400-2-222000000000000−4i4i00002i−2i2i−2i000000000000000000000000000000000
χ664-4-44400-4-440000-24-22-4-44200-2-222000000004-4000000000000000000000000000-220000000000000000
χ674-4-44400-4-440000-24-22-4-44200-2-22200000000-440000000000000000000000000002-20000000000000000
χ686666-366-3-3-366-3-300000000-3-3000000000000002200000000000000000000002220000-1-1-1-1000000-1-100
χ696666-366-3-3-366-3-300000000-3-300000000000000-2-20000000000000000000000-2-2-2000011110000001100
χ706666-366-3-3-3-6-6-3-30000000033000000000000002200000000000000000000002-2-20000-1-1-1-10000001100
χ716666-366-3-3-3-6-6-3-3000000003300000000000000-2-20000000000000000000000-22200001111000000-1-100
χ726666-3-6-6-3-3-36-63300000000-3300000000000000220000000000000000000000-22-20000-1-111000000-1100
χ736666-3-6-6-3-3-36-63300000000-3300000000000000-2-200000000000000000000002-22000011-1-10000001-100
χ746666-3-6-6-3-3-3-6633000000003-300000000000000220000000000000000000000-2-220000-1-1110000001-100
χ756666-3-6-6-3-3-3-6633000000003-300000000000000-2-2000000000000000000000022-2000011-1-1000000-1100
χ7688-8-8800-88-80000-4-44-4-4444002-2-220000000000000000000000000000000000000000000000000000000
χ778-8-88800-8-880000-4-4-4444-440022-2-20000000000000000000000000000000000000000000000000000000
χ781212-12-12-6006-66000000000000000000000000000000000000000000000000000000000000023−230000000000
χ791212-12-12-6006-660000000000000000000000000000000000000000000000000000000000000−23230000000000
χ8012-1212-12-612-12-66600-66000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6-1212-666006-6000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-60066-600000000000000000000000000004i−4i00000000000000000000000000000−2i2i000000000000
χ8312-12-1212-60066-60000000000000000000000000000−4i4i000000000000000000000000000002i−2i000000000000

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