Finite Group Databasebeta

← Group #13140527

Character table — Group #13140527

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size11112222224444444466666666121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order1222344666226666121233666666366612121212441212121266666666121244488881212121212122424242424242424226666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-111
χ51111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-111111111-1-1-1-1-11-1-111
χ81111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-11111-1-1-1-111111-111-1-1
χ92222222222222222222-122-1-12-1-1-1-1-12-12-100000022-1-1-1-1-1-1-1-100000220000000000-1-1-1-10200-1-1
χ102222222222222222222-122-1-12-1-1-1-1-12-12-100000022-1-1-1-1-1-1-1-100000-2-2000000000011110-20011
χ11222222222222222222-12-1-122-12-1-1-1-1-12-12000000-1-122-1-1-1-1-1-10002200000000-1-1-1-1000020-1-100
χ12222222222222222222-12-1-122-12-1-1-1-1-12-12000000-1-122-1-1-1-1-1-1000-2-20000000011110000-201100
χ132222222222-2-2-2-2-2-2222-122-1-12-1-1-1-1-12-12-1000000-2-2111111-1-100000220000000000-1-1-1-10-20011
χ142222222222-2-2-2-2-2-2222-122-1-12-1-1-1-1-12-12-1000000-2-2111111-1-100000-2-2000000000011110200-1-1
χ152222222222-2-2-2-2-2-222-12-1-122-12-1-1-1-1-12-1200000011-2-21111-1-10002200000000-1-1-1-10000-201100
χ162222222222-2-2-2-2-2-222-12-1-122-12-1-1-1-1-12-1200000011-2-21111-1-1000-2-2000000001111000020-1-100
χ1722222-2-2222000000-2-2222222222222-2-2-2-222222200000000-2-2-2000000-2-2000000000000000000
χ1822222-2-2222000000-2-2222222222222-2-2-2-2-2-2-2-2-2-200000000-2-2200000022000000000000000000
χ1922-2-222-22-2-20000002-222-2-2-2-2222-2-2222-2-2000000000000002-202i−2i0000002i2i−2i−2i00000000000000
χ2022-2-222-22-2-20000002-222-2-2-2-2222-2-2222-2-2000000000000002-20−2i2i000000−2i−2i2i2i00000000000000
χ2122-2-22-222-2-22-222-2-2-2222-2-2-2-2222-2-22-2-2220000002-22-222-2-2-22000000000000000000000000000
χ2222-2-22-222-2-22-222-2-2-222-1-2-2112-1-111-1-212-10000002-2-11-1-1111-100000000000000000−i3−i3i3i30000−i3i3
χ2322-2-22-222-2-22-222-2-2-222-1-2-2112-1-111-1-212-10000002-2-11-1-1111-100000000000000000i3i3−i3−i30000i3−i3
χ2422-2-22-222-2-22-222-2-2-22-1211-2-2-12-111-11-2-12000000-112-2-1-1111-10000000000000−i3−i3i3i3000000−i3i300
χ2522-2-22-222-2-22-222-2-2-22-1211-2-2-12-111-11-2-12000000-112-2-1-1111-10000000000000i3i3−i3−i3000000i3−i300
χ2622-2-22-222-2-2-22-2-222-2222-2-2-2-2222-2-22-2-222000000-22-22-2-222-22000000000000000000000000000
χ2722-2-22-222-2-2-22-2-222-222-1-2-2112-1-111-1-212-1000000-221-111-1-11-100000000000000000−i3−i3i3i30000i3−i3
χ2822-2-22-222-2-2-22-2-222-222-1-2-2112-1-111-1-212-1000000-221-111-1-11-100000000000000000i3i3−i3−i30000−i3i3
χ2922-2-22-222-2-2-22-2-222-22-1211-2-2-12-111-11-2-120000001-1-2211-1-11-10000000000000−i3−i3i3i3000000i3−i300
χ3022-2-22-222-2-2-22-2-222-22-1211-2-2-12-111-11-2-120000001-1-2211-1-11-10000000000000i3i3−i3−i3000000−i3i300
χ312-2-22200-2-2200000000222-22-2-2-222-2-200002-222-2-200000000000002−22−20000002−22−22−22−2000000
χ322-2-22200-2-2200000000222-22-2-2-222-2-200002-222-2-20000000000000−22−22000000−22−22−22−22000000
χ332-2-22200-2-2200000000222-22-2-2-222-2-20000-22-2-22200000000000002−2−220000002−22−2−22−22000000
χ342-2-22200-2-2200000000222-22-2-2-222-2-20000-22-2-2220000000000000−222−2000000−22−222−22−2000000
χ35444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-2000000-2-2-2-2111111000000000000000000000000000
χ364444444444-4-4-4-4-4-444-2-2-2-2-2-2-2-21111-2-2-2-20000002222-1-1-1-111000000000000000000000000000
χ3744444-4-4444000000-4-44-244-2-24-2-2-2-2-2-42-420000000000000022000000000000000000000000000
χ3844444-4-4444000000-4-4-24-2-244-24-2-2-2-22-42-40000000000000022000000000000000000000000000
χ3944444-4-4444000000-4-4-2-2-2-2-2-2-2-21111222200000000003-33-3-1-1000000000000000000000000000
χ4044444-4-4444000000-4-4-2-2-2-2-2-2-2-2111122220000000000-33-33-1-1000000000000000000000000000
χ4144-4-444-44-4-40000004-44-2-4-4224-2-222-24-2-4200000000000000-22000000000000000000000000000
χ4244-4-444-44-4-40000004-4-2422-4-4-24-222-2-242-400000000000000-22000000000000000000000000000
χ4344-4-444-44-4-40000004-4-2-22222-2-21-1-11-2-22200000000003-3-331-1000000000000000000000000000
χ4444-4-444-44-4-40000004-4-2-22222-2-21-1-11-2-2220000000000-333-31-1000000000000000000000000000
χ4544-4-44-444-4-44-444-4-4-44-2-22222-2-21-1-1122-2-2000000-22-2211-1-1-11000000000000000000000000000
χ4644-4-44-444-4-4-44-4-444-44-2-22222-2-21-1-1122-2-20000002-22-2-1-111-11000000000000000000000000000
χ474-44-4400-44-40000000044-44-44-4-44-44-400000000000000000000000000000000000000000000000
χ484-44-4400-44-4000000004-2-442-2-42-22-220000000000000000000000000000000000000i6−i6−i6i6000000
χ494-44-4400-44-4000000004-2-442-2-42-22-220000000000000000000000000000000000000−i6i6i6−i6000000
χ504-44-4400-44-400000000-242-2-442-4-22-22000000000000000000000000000000000i6−i6−i6i60000000000
χ514-44-4400-44-400000000-242-2-442-4-22-22000000000000000000000000000000000−i6i6i6−i60000000000
χ524-4-44400-4-44000000004-24-4-22-42-2-222000000000000000000000000022−220000000000−22−22000000
χ534-4-44400-4-44000000004-24-4-22-42-2-2220000000000000000000000000−222200000000002−22−2000000
χ544-4-44400-4-4400000000-24-224-42-4-2-2220000000000000000000000022−2200000000−22−220000000000
χ554-4-44400-4-4400000000-24-224-42-4-2-22200000000000000000000000−2222000000002−22−20000000000
χ566666-366-3-3-366-3-3-3-3-3-3000000000000000022-1-1-1-100000000002220000-1-1-1-1-1-100000000000000
χ576666-366-3-3-366-3-3-3-3-3-30000000000000000-2-211110000000000-2-2-2000011111100000000000000
χ586666-366-3-3-3-6-63333-3-3000000000000000022-1-1-1-100000000002-2-20000-1-1111100000000000000
χ596666-366-3-3-3-6-63333-3-30000000000000000-2-211110000000000-222000011-1-1-1-100000000000000
χ606666-3-6-6-3-3-300−3i33i3−3i33i333000000000000000022-1-1-1-10000000000-200000011−i3i3−i3i300000000000000
χ616666-3-6-6-3-3-300−3i33i3−3i33i3330000000000000000-2-2111100000000002000000-1-1i3−i3i3−i300000000000000
χ626666-3-6-6-3-3-3003i3−3i33i3−3i333000000000000000022-1-1-1-10000000000-200000011i3−i3i3−i300000000000000
χ636666-3-6-6-3-3-3003i3−3i33i3−3i3330000000000000000-2-2111100000000002000000-1-1−i3i3−i3i300000000000000
χ6466-6-6-36-6-33300−3i33i33i3−3i3-330000000000000000003−33−3000000000002i−2i00003−3−i−iii00000000000000
χ6566-6-6-36-6-33300−3i33i33i3−3i3-33000000000000000000−33−3300000000000−2i2i0000−33ii−i−i00000000000000
χ6666-6-6-36-6-333003i3−3i3−3i33i3-330000000000000000003−33−300000000000−2i2i00003−3ii−i−i00000000000000
χ6766-6-6-36-6-333003i3−3i3−3i33i3-33000000000000000000−33−33000000000002i−2i0000−33−i−iii00000000000000
χ6866-6-6-3-66-3336-6-3-3333-30000000000000000003−33−300000000000000000−333−3−3300000000000000
χ6966-6-6-3-66-3336-6-3-3333-3000000000000000000−33−33000000000000000003−3−333−300000000000000
χ7066-6-6-3-66-333-6633-3-33-30000000000000000003−33−300000000000000000−33−333−300000000000000
χ7166-6-6-3-66-333-6633-3-33-3000000000000000000−33−33000000000000000003−33−3−3300000000000000
χ728-88-8800-88-800000000-4-44-44-4442-22-200000000000000000000000000000000000000000000000
χ738-8-88800-8-8800000000-4-4-44-444422-2-200000000000000000000000000000000000000000000000
χ7412-1212-12-6006-660000000000000000000000000023−23−23230000000000000000000000000000000000000
χ7512-1212-12-6006-6600000000000000000000000000−232323−230000000000000000000000000000000000000
χ7612-12-1212-60066-60000000000000000000000004-4-2-2220000000000000000000000000000000000000
χ7712-12-1212-60066-6000000000000000000000000-4422-2-20000000000000000000000000000000000000

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