Finite Group Databasebeta

← Group #13148645

Character table — Group #13148645

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order1222344666241212336666666123666661212121212122222224444666666612121212122244444666612121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-1111111111111-1-1-11-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-111-1-111-1-1-1-1-1-1-1-11-11-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-111-1-1-11-1-1-1-1-1-111-1-1-1-111-11-11
χ51111111111-1-11111111111-1-11-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-11-1-11-11111111-1-111-1-1-1-1-11-11
χ61111111111-1-11111111111-1-11-1-11111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-11-1-11-1-1-111-1-11111-1-1111-11-1
χ71111111111-1-11111111111-1-11-1-11111111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-11111-1-1-1-1
χ81111111111-1-11111111111-1-11-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-11-111-1-1-1-1-1-1-1-1-1-111-1-11111
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1111111-1-1111111111-1-1-1-1-1-11-1-1-11-11111-1-1-1-1-1-1-1-111-111-1
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-11-11-11-11-1-1111111-1-1-1-1-1-11-1-11
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-111-11111-1-1-1-1111111-1-1-1-111
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-111-111-1-1-1-1-1-111-1-111111111-1-1
χ1311111-1-1111-11-1-111111111-111-1-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-11111-1-111-1-111-1-111-1-1
χ1411111-1-1111-11-1-111111111-111-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-111-1-1-11111-1-11111-1-1-1-11111-1-111
χ1511111-1-1111-11-1-111111111-111-1-1111-1-1-1-111-1-1111111111111-1-1-11-1-1111-1-1-1-1-1111-1-1-1-1-1-111-1-1111-1-11
χ1611111-1-1111-11-1-111111111-111-1-1111-1-1-1-111-1-111-1-111-1-11111-1-1-11-1-111-111-111-1-1-1-1-1111111-1-1-1-1-111-1
χ17222222222222222-1-122-1-1222-1-1-1-1-1-122-1-1-1-12222002200-1-1-1-12-1-12-1-1-1-1000200000-1-10000-1-1-1-1000000
χ18222222222222222-1-122-1-1222-1-1-1-1-1-122-1-1-1-1-2-2-2-200-2-20011112-1-12-1-1-1-1000-2000001100001111000000
χ1922222222222222-122-1-122-122-122-1-1-1-1-1222200000000220000-1-1-1-1-1-1-1-10220002000000-1-10000-1-10-10-1
χ2022222222222222-122-1-122-122-122-1-1-1-1-1222200000000-2-20000-1-1-1-1-1-1-1-10-2-2000-2000000110000110101
χ212222222222-2-2222-1-122-1-12-2-2-111-1-1-122-1-11122-2-20022001111-211-2-1-111000-200000-1-10000-1-111000000
χ222222222222-2-2222-1-122-1-12-2-2-111-1-1-122-1-111-2-22200-2-200-1-1-1-1-211-2-1-11100020000011000011-1-1000000
χ232222222222-2-222-122-1-122-1-2-2-1-2-2-1-1-1-1-122-2-2000000002200001111-1-1110-22000-2000000-1-10000-1-10101
χ242222222222-2-222-122-1-122-1-2-2-1-2-2-1-1-1-1-122-2-200000000-2-200001111-1-11102-20002000000110000110-10-1
χ2522222-2-22222-2-2-22-1-122-1-122-2-1-1-1-1-1-1-2-21111222200-2-200-1-1-1-12-1-1-21111000-200000-1-100001111000000
χ2622222-2-22222-2-2-22-1-122-1-122-2-1-1-1-1-1-1-2-21111-2-2-2-200220011112-1-1-21111000200000110000-1-1-1-1000000
χ2722222-2-22222-2-2-2-122-1-122-12-2-122-1-1-111-2-2-2-200000000220000-1-1-11111102-2000-2000000110000-1-10-101
χ2822222-2-22222-2-2-2-122-1-122-12-2-122-1-1-111-2-2-2-200000000-2-20000-1-1-1111110-220002000000-1-1000011010-1
χ2922222-2-2222-22-2-22-1-122-1-12-22-111-1-1-1-2-211-1-122-2-200-2-2001111-211211-1-1000200000-1-1000011-1-1000000
χ3022222-2-2222-22-2-22-1-122-1-12-22-111-1-1-1-2-211-1-1-2-222002200-1-1-1-1-211211-1-1000-200000110000-1-111000000
χ3122222-2-2222-22-2-2-122-1-122-1-22-1-2-2-1-1-111-2-22200000000220000111-111-1-10-2-20002000000110000-1-1010-1
χ3222222-2-2222-22-2-2-122-1-122-1-22-1-2-2-1-1-111-2-22200000000-2-20000111-111-1-1022000-2000000-1-10000110-101
χ3322-2-222i−2i2-2-2002i−2i222-22-2-2-2002002-2-22i−2i2i−2i002-200002i−2i00000000002i−2i000000000002-200002i−2i00000000
χ3422-2-222i−2i2-2-2002i−2i222-22-2-2-2002002-2-22i−2i2i−2i00-220000−2i2i00000000002i−2i00000000000-220000−2i2i00000000
χ3522-2-222i−2i2-2-2002i−2i2-1-1-2211-200-1−i3i3-1112i−2i−ii3−32-200002i−2i00−i3−i3i3i30−i3i30−ii3−3000000000-110000−ii3−3000000
χ3622-2-222i−2i2-2-2002i−2i2-1-1-2211-200-1−i3i3-1112i−2i−ii3−3-220000−2i2i00i3i3−i3−i30−i3i30−ii3−30000000001-10000i−i−33000000
χ3722-2-222i−2i2-2-2002i−2i2-1-1-2211-200-1i3−i3-1112i−2i−ii−332-200002i−2i00i3i3−i3−i30i3−i30−ii−33000000000-110000−ii−33000000
χ3822-2-222i−2i2-2-2002i−2i2-1-1-2211-200-1i3−i3-1112i−2i−ii−33-220000−2i2i00−i3−i3i3i30i3−i30−ii−330000000001-10000i−i3−3000000
χ3922-2-22−2i2i2-2-200−2i2i222-22-2-2-2002002-2-2−2i2i−2i2i002-20000−2i2i0000000000−2i2i000000000002-20000−2i2i00000000
χ4022-2-22−2i2i2-2-200−2i2i222-22-2-2-2002002-2-2−2i2i−2i2i00-2200002i−2i0000000000−2i2i00000000000-2200002i−2i00000000
χ4122-2-22−2i2i2-2-200−2i2i2-1-1-2211-200-1−i3i3-111−2i2ii−i−332-20000−2i2i00−i3−i3i3i30−i3i30i−i−33000000000-110000i−i−33000000
χ4222-2-22−2i2i2-2-200−2i2i2-1-1-2211-200-1−i3i3-111−2i2ii−i−33-2200002i−2i00i3i3−i3−i30−i3i30i−i−330000000001-10000−ii3−3000000
χ4322-2-22−2i2i2-2-200−2i2i2-1-1-2211-200-1i3−i3-111−2i2ii−i3−32-20000−2i2i00i3i3−i3−i30i3−i30i−i3−3000000000-110000i−i3−3000000
χ4422-2-22−2i2i2-2-200−2i2i2-1-1-2211-200-1i3−i3-111−2i2ii−i3−3-2200002i−2i00−i3−i3i3i30i3−i30i−i3−30000000001-10000−ii−33000000
χ452-2-22200-22-2000022-2-2-22-2200200-22-2000000002-22-2002-22-22-20000000000000002-200000000002-20000
χ462-2-22200-22-2000022-2-2-22-2200200-22-2000000002-2-2200-222-22-2000000000000000-220000000000-220000
χ472-2-22200-22-2000022-2-2-22-2200200-22-200000000-222-200-22-22-220000000000000002-20000000000-220000
χ482-2-22200-22-2000022-2-2-22-2200200-22-200000000-22-22002-2-22-22000000000000000-2200000000002-20000
χ4944444444444444-2-2-2-2-2-2-2-2441-2-2111-2-2-2-2-2-200000000000000-211-211110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-4122111-2-2-2-222000000000000002-1-1211-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-211122222200000000000000-2112-1-1-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-441221112222-2-2000000000000002-1-1-2-1-1110000000000000000000000000
χ5344-4-444i−4i4-4-4004i−4i-2442-2-4-4200-200-222−2i2i4i−4i00000000000000000000−2i2i000000000000000000000000000
χ5444-4-444i−4i4-4-4004i−4i-2-2-22-2222001−2i32i31-1-1−2i2i−2i2i23−23000000000000000i3−i30i−i−330000000000000000000000000
χ5544-4-444i−4i4-4-4004i−4i-2-2-22-22220012i3−2i31-1-1−2i2i−2i2i−2323000000000000000−i3i30i−i3−30000000000000000000000000
χ5644-4-44−4i4i4-4-400−4i4i-2442-2-4-4200-200-2222i−2i−4i4i000000000000000000002i−2i000000000000000000000000000
χ5744-4-44−4i4i4-4-400−4i4i-2-2-22-2222001−2i32i31-1-12i−2i2i−2i−2323000000000000000i3−i30−ii3−30000000000000000000000000
χ5844-4-44−4i4i4-4-400−4i4i-2-2-22-22220012i3−2i31-1-12i−2i2i−2i23−23000000000000000−i3i30−ii−330000000000000000000000000
χ594-44-4400-4-44000044-44-4-44-400400-4-4400000000000000000000000000000000000000000000000000000
χ604-44-4400-4-4400004-224-42-2-400-20022-20000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ614-44-4400-4-4400004-224-42-2-400-20022-200000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ624-44-4400-4-440000-24-4-22-44200-20022-20000000000000000000000000000000000000000023−230000000000
χ634-44-4400-4-440000-24-4-22-44200-20022-200000000000000000000000000000000000000000−23230000000000
χ644-4-44400-44-400004-22-4-4-22400-2002-22000000004-4000000-22-22000000000000000000000000000000000
χ654-4-44400-44-400004-22-4-4-22400-2002-2200000000-440000002-22-2000000000000000000000000000000000
χ664-4-44400-44-40000-24-4224-4-200-2002-22000000000000004-40000000000000000000000000000000-220000
χ674-4-44400-44-40000-24-4224-4-200-2002-2200000000000000-4400000000000000000000000000000002-20000
χ686666-366-3-3-366-3-300000000-3-300000000000000002200000000000000002000220-1-100-1-100000000-10-10
χ696666-366-3-3-366-3-300000000-3-30000000000000000-2-20000000000000000-2000-2-20110011000000001010
χ706666-366-3-3-3-6-6-3-300000000330000000000000000220000000000000000-20002-20-1-100-1-1000000001010
χ716666-366-3-3-3-6-6-3-300000000330000000000000000-2-200000000000000002000-22011001100000000-10-10
χ726666-3-6-6-3-3-36-63300000000-330000000000000000220000000000000000-2000-220-1-100110000000010-10
χ736666-3-6-6-3-3-36-63300000000-330000000000000000-2-2000000000000000020002-201100-1-100000000-1010
χ746666-3-6-6-3-3-3-6633000000003-300000000000000002200000000000000002000-2-20-1-1001100000000-1010
χ756666-3-6-6-3-3-3-6633000000003-30000000000000000-2-20000000000000000-20002201100-1-10000000010-10
χ768-88-8800-8-880000-4-44-444-4400200-2-2200000000000000000000000000000000000000000000000000000
χ778-8-88800-88-80000-4-4444-44-400200-22-200000000000000000000000000000000000000000000000000000
χ781212-12-12-612i−12i-66600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ791212-12-12-6−12i12i-666006i−6i000000000000000000000000000000000000000000000000000000000000000000000
χ8012-1212-12-60066-600000000000000000000000000000000000000000000000000000000000−2i32i3000000000000
χ8112-1212-12-60066-6000000000000000000000000000000000000000000000000000000000002i3−2i3000000000000
χ8212-12-1212-6006-660000000000000000000000000000004-400000000000000000000000-220000000000000000
χ8312-12-1212-6006-66000000000000000000000000000000-44000000000000000000000002-20000000000000000

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