Finite Group Databasebeta

← Group #13148722

Character table — Group #13148722

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12223446662412123366666661236666612121212121222441212121266612121212122224444444666612121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11-11-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-11-1-1-111-1-1-1-1-1-1-1-111-1-111-11-11
χ51111111111-1-11111111111-1-11-1-111111-1-11111111111-1-1-1-111-1-11-11-1-1-11-11-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-11111111111-1-11-1-111111-1-11111111111-1-1-1-111-1-1-11-1-11-1-11-11111111-1-111-1-111-1-1-1-1
χ71111111111-1-11111111111-1-11-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11111-1-11-1-1-1-1-1-1111111111-11-1
χ81111111111-1-11111111111-1-11-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-11-111-111-1-11111-1-111-1-1-11-11
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-11-111-1-1-11-11-1-1111111-1-1-1-11111-1-1
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-11-111-11-11-11111-1-11111-1-1-1-1-1-111
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11-1-1-111-111-1-1-1-1-111-1-11111-1-11-1-11
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-111-1-1111-1-1-1-1-1-1-1-11111-111-1
χ1311111-1-1111-11-1-111111111-111-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-111111-111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ1411111-1-1111-11-1-111111111-111-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-111111-1-11111-1-1-1-11111-1-111
χ1511111-1-1111-11-1-111111111-111-1-1111-1-111-1-1-1-1111111-1-1-11-1-11111-11-1-1-1-11111-1-1-1-111-1-1-1-1111-1-11
χ1611111-1-1111-11-1-111111111-111-1-1111-1-111-1-1-1-1111111-1-1-11-1-111-1-1111-111-1-1-1-1-1-1111111-1-1-1-1-111-1
χ17222222222222222-12-12-12-122-122-1-1-1-1-1222200000000-1-1-1-1-1-1-1-1002020002200000000-1-100-1-10-10-1
χ18222222222222222-12-12-12-122-122-1-1-1-1-1222200000000-1-1-1-1-1-1-1-100-20-2000-2-2000000001100110101
χ1922222222222222-12-12-12-1222-1-1-1-1-1-122-1-1-1-12222-1-1-1-12-1-12-1-1-1-1000202000000-1-100-1-100-1-1000000
χ2022222222222222-12-12-12-1222-1-1-1-1-1-122-1-1-1-1-2-2-2-211112-1-12-1-1-1-1000-20-20000001100110011000000
χ212222222222-2-2222-12-12-12-1-2-2-1-2-2-1-1-1-1-1-2-222000000001111-1-1110020-20002-2000000001100110-10-1
χ222222222222-2-2222-12-12-12-1-2-2-1-2-2-1-1-1-1-1-2-222000000001111-1-11100-202000-2200000000-1-100-1-10101
χ232222222222-2-222-12-12-12-12-2-2-111-1-1-12211-1-12222-1-1-1-1-211-2-1-111000-20-2000000-1-100110011000000
χ242222222222-2-222-12-12-12-12-2-2-111-1-1-12211-1-1-2-2-2-21111-211-2-1-1110002020000001100-1-100-1-1000000
χ2522222-2-22222-2-2-22-12-12-12-12-2-122-1-1-111-2-2-2-200000000-1-1-1111110020-2000-22000000001100-1-10-101
χ2622222-2-22222-2-2-22-12-12-12-12-2-122-1-1-111-2-2-2-200000000-1-1-11111100-2020002-200000000-1-10011010-1
χ2722222-2-22222-2-2-2-12-12-12-122-2-1-1-1-1-1-1-2-2111122-2-211112-1-1-2111100020-2000000-1-100-1-10011000000
χ2822222-2-22222-2-2-2-12-12-12-122-2-1-1-1-1-1-1-2-21111-2-222-1-1-1-12-1-1-21111000-20200000011001100-1-1000000
χ2922222-2-2222-22-2-22-12-12-12-1-22-1-2-2-1-1-11122-2-200000000111-111-1-100202000-2-200000000-1-100110-101
χ3022222-2-2222-22-2-22-12-12-12-1-22-1-2-2-1-1-11122-2-200000000111-111-1-100-20-200022000000001100-1-1010-1
χ3122222-2-2222-22-2-2-12-12-12-12-22-111-1-1-1-2-2-1-11122-2-21111-211211-1-1000-202000000-1-1001100-1-1000000
χ3222222-2-2222-22-2-2-12-12-12-12-22-111-1-1-1-2-2-1-111-2-222-1-1-1-1-211211-1-100020-20000001100-1-10011000000
χ3322-2-222i−2i2-2-2002i−2i22-2-222-2-2002002-2-22i−2i002i−2i2-22i−2i2i2i−2i−2i00002i−2i000000000000002-200000000000000
χ3422-2-222i−2i2-2-2002i−2i22-2-222-2-2002002-2-22i−2i002i−2i-22−2i2i−2i−2i2i2i00002i−2i00000000000000-2200000000000000
χ3522-2-222i−2i2-2-2002i−2i-121-2-121-200-1−i3i3-1112i−2i3−3−ii2-22i−2i−i−iii0−i3i30−ii3−3000000000000-1100−i3i3003−3000000
χ3622-2-222i−2i2-2-2002i−2i-121-2-121-200-1−i3i3-1112i−2i3−3−ii-22−2i2iii−i−i0−i3i30−ii3−30000000000001-100i3−i300−33000000
χ3722-2-222i−2i2-2-2002i−2i-121-2-121-200-1i3−i3-1112i−2i−33−ii2-22i−2i−i−iii0i3−i30−ii−33000000000000-1100i3−i300−33000000
χ3822-2-222i−2i2-2-2002i−2i-121-2-121-200-1i3−i3-1112i−2i−33−ii-22−2i2iii−i−i0i3−i30−ii−330000000000001-100−i3i3003−3000000
χ3922-2-22−2i2i2-2-200−2i2i22-2-222-2-2002002-2-2−2i2i00−2i2i2-2−2i2i−2i−2i2i2i0000−2i2i000000000000002-200000000000000
χ4022-2-22−2i2i2-2-200−2i2i22-2-222-2-2002002-2-2−2i2i00−2i2i-222i−2i2i2i−2i−2i0000−2i2i00000000000000-2200000000000000
χ4122-2-22−2i2i2-2-200−2i2i-121-2-121-200-1−i3i3-111−2i2i−33i−i2-2−2i2iii−i−i0−i3i30i−i−33000000000000-1100−i3i300−33000000
χ4222-2-22−2i2i2-2-200−2i2i-121-2-121-200-1−i3i3-111−2i2i−33i−i-222i−2i−i−iii0−i3i30i−i−330000000000001-100i3−i3003−3000000
χ4322-2-22−2i2i2-2-200−2i2i-121-2-121-200-1i3−i3-111−2i2i3−3i−i2-2−2i2iii−i−i0i3−i30i−i3−3000000000000-1100i3−i3003−3000000
χ4422-2-22−2i2i2-2-200−2i2i-121-2-121-200-1i3−i3-111−2i2i3−3i−i-222i−2i−i−iii0i3−i30i−i3−30000000000001-100−i3i300−33000000
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2-2-2-2-200000000-211-211110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-4122111-2-222-2-2000000002-1-1211-1-10000000000000000000000000000
χ4744444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-211122222200000000-2112-1-1-1-10000000000000000000000000000
χ4844444-4-4444-44-4-4-2-2-2-2-2-2-2-2-4412211122-2-222000000002-1-1-2-1-1110000000000000000000000000000
χ4944-4-444i−4i4-4-4004i−4i4-2-424-2-4200-200-222−2i2i004i−4i000000000000−2i2i000000000000000000000000000000
χ5044-4-444i−4i4-4-4004i−4i-2-222-2-222001−2i32i31-1-1−2i2i23−23−2i2i000000000i3−i30i−i−330000000000000000000000000000
χ5144-4-444i−4i4-4-4004i−4i-2-222-2-2220012i3−2i31-1-1−2i2i−2323−2i2i000000000−i3i30i−i3−30000000000000000000000000000
χ5244-4-44−4i4i4-4-400−4i4i4-2-424-2-4200-200-2222i−2i00−4i4i0000000000002i−2i000000000000000000000000000000
χ5344-4-44−4i4i4-4-400−4i4i-2-222-2-222001−2i32i31-1-12i−2i−23232i−2i000000000i3−i30−ii3−30000000000000000000000000000
χ5444-4-44−4i4i4-4-400−4i4i-2-222-2-2220012i3−2i31-1-12i−2i23−232i−2i000000000−i3i30−ii−330000000000000000000000000000
χ554-44-4400-44-4000044-44-4-44-400400-44-400000000000000000000000000000000000000000000000000
χ564-44-4400-44-400004-2-4-2-424200-2002-22000000000000000000000000000000000000000023−2300000000
χ574-44-4400-44-400004-2-4-2-424200-2002-220000000000000000000000000000000000000000−232300000000
χ584-44-4400-44-40000-24242-4-2-400-2002-220000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ594-44-4400-44-40000-24242-4-2-400-2002-2200000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ604-4-44400-4-440000444-4-4-4-4400400-4-4400000000000000000000000000000000000000000000000000
χ614-4-44400-4-4400004-242-42-4-200-20022-200000000000000000000000000000000000000000000−2i32i30000
χ624-4-44400-4-4400004-242-42-4-200-20022-2000000000000000000000000000000000000000000002i3−2i30000
χ634-4-44400-4-440000-24-2-42-42400-20022-2000000000023−23−2323000000000000000000000000000000000000
χ644-4-44400-4-440000-24-2-42-42400-20022-20000000000−232323−23000000000000000000000000000000000000
χ656666-366-3-3-366-3-300000000-3-300000000000000000000000000002200002200-1-100-1-100000000-10-10
χ666666-366-3-3-366-3-300000000-3-30000000000000000000000000000-2-20000-2-200110011000000001010
χ676666-366-3-3-3-6-6-3-3000000003300000000000000000000000000002-200002-20011001100000000-10-10
χ686666-366-3-3-3-6-6-3-300000000330000000000000000000000000000-220000-2200-1-100-1-1000000001010
χ696666-3-6-6-3-3-36-63300000000-3300000000000000000000000000002-20000-22001100-1-100000000-1010
χ706666-3-6-6-3-3-36-63300000000-330000000000000000000000000000-2200002-200-1-100110000000010-10
χ716666-3-6-6-3-3-3-6633000000003-30000000000000000000000000000220000-2-200-1-1001100000000-1010
χ726666-3-6-6-3-3-3-6633000000003-30000000000000000000000000000-2-2000022001100-1-10000000010-10
χ738-88-8800-88-80000-4-44-444-4400200-22-200000000000000000000000000000000000000000000000000
χ748-8-88800-8-880000-4-4-44444-400200-2-2200000000000000000000000000000000000000000000000000
χ751212-12-12-612i−12i-66600−6i6i000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-6−12i12i-666006i−6i000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212-12-6006-6600000000000000000000000000000000000000000000000000000000−2i32i3000000000000
χ7812-1212-12-6006-66000000000000000000000000000000000000000000000000000000002i3−2i3000000000000
χ7912-12-1212-60066-60000000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ8012-12-1212-60066-600000000000000000000000000000000000000000000000000002i3−2i30000000000000000

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