Finite Group Databasebeta

← Group #13148693

Character table — Group #13148693

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order122234466624121233666666612366666121212121212224444444412121212666121212121222444446666121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11111-1-1111111111111-1-1-11-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-111-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111-1-11111111111-1-11-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-1-1111111-1-1-1-1-1-111-1-111
χ61111111111-1-11111111111-1-11-1-11111111-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-11-1-1-111-1-111-1-1-1-111111111-1-1
χ71111111111-1-11111111111-1-11-1-11111111-1-1-1-111-1-111111111-1-1-1-111-1-11-1-11-11-111-1-111111111-1-1-1-1-1-1
χ81111111111-1-11111111111-1-11-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-11111-11-1-1-1-1-1-111-1-1-1-1-1-11111
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-11-1-1-1111111-1-111-1-11-11-1
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-11-1-111-111111-1-11111-1-1-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-111-1-111-1-1111-1-11
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-1-11-11-1-11111-1-1-1-1-1-1-1-11111-111-1
χ1311111-1-1111-11-1-111111111-111-1-1111-1-1-1-1111111-1-111111111-1-1-11-1-111-1-11-1-1-11-1-11111-1-111-1-1-1-1-111-1
χ1411111-1-1111-11-1-111111111-111-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-11-1-11111-1-111-11111-1-1-1-1-1-111-1-11-1-11
χ1511111-1-1111-11-1-111111111-111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-11111-1-1-1-11111-1-11111-11-11
χ1611111-1-1111-11-1-111111111-111-1-1111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-11-1-1111111-1-1-111-1-1-1-11111-1-1111-11-1
χ17222222222222222-1-1-1222-122-1-1-1-1-1-1-1-122-1-12200222200-1-1-1-12-1-12-1-1-1-1000200000-1-100-1-10000-1-10000
χ18222222222222222-1-1-1222-122-1-1-1-1-1-1-1-122-1-1-2-200-2-2-2-20011112-1-12-1-1-1-1000-2000001100110000110000
χ1922222222222222-1222-1-1-1222-122-1-1-122-1-12200000000220000-1-1-1-1-1-1-1-1002022000000000-1-1-1-10000-1-1
χ2022222222222222-1222-1-1-1222-122-1-1-122-1-12200000000-2-20000-1-1-1-1-1-1-1-100-20-2-20000000001111000011
χ212222222222-2-2222-1-1-1222-1-2-2-111-1-1-1-1-12211220022-2-2001111-211-2-1-111000-200000-1-100110000-1-10000
χ222222222222-2-2222-1-1-1222-1-2-2-111-1-1-1-1-12211-2-200-2-22200-1-1-1-1-211-2-1-1110002000001100-1-10000110000
χ232222222222-2-222-1222-1-1-12-2-2-1-2-2-1-1-122-1-1-2-2000000002200001111-1-11100-20-22000000000-1-1-1-1000011
χ242222222222-2-222-1222-1-1-12-2-2-1-2-2-1-1-122-1-1-2-200000000-2-200001111-1-11100202-200000000011110000-1-1
χ2522222-2-22222-2-2-22-1-1-1222-12-2-1-1-1-1-1-111-2-2112200-2-2-2-20011112-1-1-21111000200000-1-100-1-10000110000
χ2622222-2-22222-2-2-22-1-1-1222-12-2-1-1-1-1-1-111-2-211-2-200222200-1-1-1-12-1-1-21111000-2000001100110000-1-10000
χ2722222-2-22222-2-2-2-1222-1-1-122-2-122-1-1-1-2-211-2-200000000220000-1-1-11111100-202-2000000000-1-11100001-1
χ2822222-2-22222-2-2-2-1222-1-1-122-2-122-1-1-1-2-211-2-200000000-2-20000-1-1-1111110020-2200000000011-1-10000-11
χ2922222-2-2222-22-2-22-1-1-1222-1-22-111-1-1-111-2-2-1-12200-2-22200-1-1-1-1-211211-1-1000-200000-1-100110000110000
χ3022222-2-2222-22-2-22-1-1-1222-1-22-111-1-1-111-2-2-1-1-2-20022-2-2001111-211211-1-10002000001100-1-10000-1-10000
χ3122222-2-2222-22-2-2-1222-1-1-12-22-1-2-2-1-1-1-2-2112200000000220000111-111-1-10020-2-2000000000-1-1110000-11
χ3222222-2-2222-22-2-2-1222-1-1-12-22-1-2-2-1-1-1-2-2112200000000-2-20000111-111-1-100-202200000000011-1-100001-1
χ3322-2-2200-22-20000222-22-2-2-200200-22-2000000002-2002i−2i2i−2i2i2i−2i−2i00000000000000000002-2002i−2i00000000
χ3422-2-2200-22-20000222-22-2-2-200200-22-2000000002-200−2i2i−2i2i−2i−2i2i2i00000000000000000002-200−2i2i00000000
χ3522-2-2200-22-20000222-22-2-2-200200-22-200000000-22002i−2i−2i2i2i2i−2i−2i0000000000000000000-2200−2i2i00000000
χ3622-2-2200-22-20000222-22-2-2-200200-22-200000000-2200−2i2i2i−2i−2i−2i2i2i0000000000000000000-22002i−2i00000000
χ372-22-222i−2i2-2-2002i−2i22-22-2-22-2002002-2-22i−2i2i−2i002-2002i−2i0000000000002i−2i000000000002-2000000002i−2i0000
χ382-22-222i−2i2-2-2002i−2i22-22-2-22-2002002-2-22i−2i2i−2i00-2200−2i2i0000000000002i−2i00000000000-2200000000−2i2i0000
χ392-22-222i−2i2-2-2002i−2i2-11-1-2-22100-1−i3i3-111−ii2i−2i3−32-2002i−2i00003−33−30−i3i30−ii3−3000000000-1100−i3i30000−ii0000
χ402-22-222i−2i2-2-2002i−2i2-11-1-2-22100-1−i3i3-111−ii2i−2i3−3-2200−2i2i0000−33−330−i3i30−ii3−30000000001-100i3−i30000i−i0000
χ412-22-222i−2i2-2-2002i−2i2-11-1-2-22100-1i3−i3-111−ii2i−2i−332-2002i−2i0000−33−330i3−i30−ii−33000000000-1100i3−i30000−ii0000
χ422-22-222i−2i2-2-2002i−2i2-11-1-2-22100-1i3−i3-111−ii2i−2i−33-2200−2i2i00003−33−30i3−i30−ii−330000000001-100−i3i30000i−i0000
χ432-22-22−2i2i2-2-200−2i2i22-22-2-22-2002002-2-2−2i2i−2i2i002-200−2i2i000000000000−2i2i000000000002-200000000−2i2i0000
χ442-22-22−2i2i2-2-200−2i2i22-22-2-22-2002002-2-2−2i2i−2i2i00-22002i−2i000000000000−2i2i00000000000-22000000002i−2i0000
χ452-22-22−2i2i2-2-200−2i2i2-11-1-2-22100-1−i3i3-111i−i−2i2i−332-200−2i2i0000−33−330−i3i30i−i−33000000000-1100−i3i30000i−i0000
χ462-22-22−2i2i2-2-200−2i2i2-11-1-2-22100-1−i3i3-111i−i−2i2i−33-22002i−2i00003−33−30−i3i30i−i−330000000001-100i3−i30000−ii0000
χ472-22-22−2i2i2-2-200−2i2i2-11-1-2-22100-1i3−i3-111i−i−2i2i3−32-200−2i2i00003−33−30i3−i30i−i3−3000000000-1100i3−i30000i−i0000
χ482-22-22−2i2i2-2-200−2i2i2-11-1-2-22100-1i3−i3-111i−i−2i2i3−3-22002i−2i0000−33−330i3−i30i−i3−30000000001-100−i3i30000−ii0000
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
χ5344-4-4400-44-400004-2-224-4-4200-2002-220000000000004i−4i00−2i−2i2i2i000000000000000000000000000000000
χ5444-4-4400-44-400004-2-224-4-4200-2002-22000000000000−4i4i002i2i−2i−2i000000000000000000000000000000000
χ5544-4-4400-44-40000-244-4-222-400-2002-22000000000000004i−4i000000000000000000000000000−2i2i00000000
χ5644-4-4400-44-40000-244-4-222-400-2002-2200000000000000−4i4i0000000000000000000000000002i−2i00000000
χ574-44-444i−4i4-4-4004i−4i-24-4422-2-400-200-2224i−4i−2i2i00000000000000000000−2i2i000000000000000000000000000
χ584-44-444i−4i4-4-4004i−4i-2-22-222-22001−2i32i31-1-1−2i2i−2i2i23−23000000000000000i3−i30i−i−330000000000000000000000000
χ594-44-444i−4i4-4-4004i−4i-2-22-222-220012i3−2i31-1-1−2i2i−2i2i−2323000000000000000−i3i30i−i3−30000000000000000000000000
χ604-44-44−4i4i4-4-400−4i4i-24-4422-2-400-200-222−4i4i2i−2i000000000000000000002i−2i000000000000000000000000000
χ614-44-44−4i4i4-4-400−4i4i-2-22-222-22001−2i32i31-1-12i−2i2i−2i−2323000000000000000i3−i30−ii3−30000000000000000000000000
χ624-44-44−4i4i4-4-400−4i4i-2-22-222-220012i3−2i31-1-12i−2i2i−2i23−23000000000000000−i3i30−ii−330000000000000000000000000
χ634-4-44400-4-44000044-4-4-44-4400400-4-4400000000000000000000000000000000000000000000000000000
χ644-4-44400-4-4400004-222-44-4-200-20022-20000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ654-4-44400-4-4400004-222-44-4-200-20022-200000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ664-4-44400-4-440000-24-4-42-22400-20022-200000000000000000000000000000000000000000000023−23000000
χ674-4-44400-4-440000-24-4-42-22400-20022-2000000000000000000000000000000000000000000000−2323000000
χ686666-366-3-3-366-3-300000000-3-300000000000000220000000000000000002200002-1-100-1-100000000-1-100
χ696666-366-3-3-366-3-300000000-3-300000000000000-2-2000000000000000000-2-20000-2110011000000001100
χ706666-366-3-3-3-6-6-3-3000000003300000000000000220000000000000000002-20000-2-1-100-1-1000000001100
χ716666-366-3-3-3-6-6-3-3000000003300000000000000-2-2000000000000000000-220000211001100000000-1-100
χ726666-3-6-6-3-3-36-63300000000-330000000000000022000000000000000000-220000-21100-1-100000000-1100
χ736666-3-6-6-3-3-36-63300000000-3300000000000000-2-20000000000000000002-200002-1-10011000000001-100
χ746666-3-6-6-3-3-3-6633000000003-30000000000000022000000000000000000-2-2000021100-1-1000000001-100
χ756666-3-6-6-3-3-3-6633000000003-300000000000000-2-2000000000000000000220000-2-1-1001100000000-1100
χ7688-8-8800-88-80000-4-4-44-444400200-22-200000000000000000000000000000000000000000000000000000
χ778-8-88800-8-880000-4-4444-44-400200-2-2200000000000000000000000000000000000000000000000000000
χ781212-12-12-6006-6600000000000000000000000000004-400000000000000000000000000000-22000000000000
χ791212-12-12-6006-660000000000000000000000000000-44000000000000000000000000000002-2000000000000
χ8012-1212-12-612i−12i-66600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6−12i12i-666006i−6i000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-60066-60000000000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ8312-12-1212-60066-600000000000000000000000000000000000000000000000000000002i3−2i30000000000000000

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