Finite Group Databasebeta

← Group #13148524

Character table — Group #13148524

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order12223446662466121212123366666636661212121244441212121266661212121212122244444444661212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-11-11-1-1-111-1-1-1-1-1-1-111-1-1-1-1111-1-11
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-111-1-1-11-1-1-1-1-1-1-1-11111-1-1-111-1
χ51111111111-1-1-1-111-1-1111111111111111111111111-1-1-1-1-1-111-1-1-111-11-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ61111111111-1-1-1-111-1-1111111111111111111111111-1-1-1-1-1-111-1-1-1-1-11-11-1-111-1-111-1-111111111-1-1-1-1
χ71111111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1111-1111-1-111-1-11111-1-11-1-11
χ81111111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1111-11-11-111-1-11111-1-1-1-111-111-1
χ911111-1-11111-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-1-1-1111111-1-1-1-111-1-1111-11-1
χ1011111-1-11111-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-111-11-11-1-11111-1-111-1-111-1-1-11-11
χ1111111-1-11111-111-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-111-11-1-1-1-1-111-1-1-1-1111111-1-1
χ1211111-1-11111-111-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-111-11-1-1-1-1111111-1-1-1-1-1-111
χ1311111-1-1111-11-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-11-11111-1-1-1-1-1111111-1-111-1-11-11-1
χ1411111-1-1111-11-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1-11111-1-11111-1-111-1-111-11-11
χ1511111-1-1111-11-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1
χ1611111-1-1111-11-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1-1-111-111-111-1-1-1-1-1-1-1-11111-1-111
χ172222222222222222222-1-1-1222-1-1-1-1-1-1-122000000002-1-1-12-1-1-1-1-10202000220000000-1-10000-1-1-100-1
χ182222222222222222222-1-1-1222-1-1-1-1-1-1-122000000002-1-1-12-1-1-1-1-10-20-2000-2-20000000110000111001
χ19222222222222222222-1222-1-1-12-1-1-1-122-1-100000000-12-1-1-12-1-1-1-1002022000200000000-1-1-1-1000-1-10
χ20222222222222222222-1222-1-1-12-1-1-1-122-1-100000000-12-1-1-12-1-1-1-100-20-2-2000-2000000001111000110
χ212222222222-2-2-2-222-2-22-1-1-1222-1-1-1-1-1-1-12200000000-2111-21-1-111020-20002-2000000011000011-100-1
χ222222222222-2-2-2-222-2-22-1-1-1222-1-1-1-1-1-1-12200000000-2111-21-1-1110-202000-220000000-1-10000-1-11001
χ232222222222-2-2-2-222-2-2-1222-1-1-12-1-1-1-122-1-1000000001-2111-2-1-11100202-2000-2000000001111000-1-10
χ242222222222-2-2-2-222-2-2-1222-1-1-12-1-1-1-122-1-1000000001-2111-2-1-11100-20-22000200000000-1-1-1-1000110
χ2522222-2-22222-222-2-2-2-22-1-1-1222-1-1-1-1-111-2-2000000002-1-1-1-211111020-2000-220000000110000-1-1-1001
χ2622222-2-22222-222-2-2-2-22-1-1-1222-1-1-1-1-111-2-2000000002-1-1-1-2111110-2020002-20000000-1-1000011100-1
χ2722222-2-22222-222-2-2-2-2-1222-1-1-12-1-1-1-1-2-21100000000-12-1-11-211110020-22000-20000000011-1-1000-110
χ2822222-2-22222-222-2-2-2-2-1222-1-1-12-1-1-1-1-2-21100000000-12-1-11-2111100-202-2000200000000-1-1110001-10
χ2922222-2-2222-22-2-2-2-2222-1-1-1222-1-1-1-1-111-2-200000000-21112-111-1-10202000-2-20000000-1-1000011-1001
χ3022222-2-2222-22-2-2-2-2222-1-1-1222-1-1-1-1-111-2-200000000-21112-111-1-10-20-2000220000000110000-1-1100-1
χ3122222-2-2222-22-2-2-2-222-1222-1-1-12-1-1-1-1-2-211000000001-211-1211-1-10020-2-2000200000000-1-111000-110
χ3222222-2-2222-22-2-2-2-222-1222-1-1-12-1-1-1-1-2-211000000001-211-1211-1-100-2022000-20000000011-1-10001-10
χ332-22-222i−2i-22-200002i−2i0022-22-2-22-222-2-22i−2i2i−2i2-22i−2i2i2i−2i−2i0000002i−2i000000000000002-200000000000000
χ342-22-222i−2i-22-200002i−2i0022-22-2-22-222-2-22i−2i2i−2i-22−2i2i−2i−2i2i2i0000002i−2i00000000000000-2200000000000000
χ352-22-22−2i2i-22-20000−2i2i0022-22-2-22-222-2-2−2i2i−2i2i2-2−2i2i−2i−2i2i2i000000−2i2i000000000000002-200000000000000
χ362-22-22−2i2i-22-20000−2i2i0022-22-2-22-222-2-2−2i2i−2i2i-222i−2i2i2i−2i−2i000000−2i2i00000000000000-2200000000000000
χ37444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-200000000-2-211-2-211110000000000000000000000000000
χ384444444444-4-4-4-444-4-4-2-2-2-2-2-2-2-21111-2-2-2-20000000022-1-12211-1-10000000000000000000000000000
χ3944444-4-44444-444-4-4-4-4-2-2-2-2-2-2-2-21111222200000000-2-21122-1-1-1-10000000000000000000000000000
χ4044444-4-4444-44-4-4-4-444-2-2-2-2-2-2-2-2111122220000000022-1-1-2-2-1-1110000000000000000000000000000
χ4144-4-44004-4-400000000444-44-4-4-44-44-400000000000000000000000000000000000000000000000000
χ4244-4-44004-4-4000000004-2-224-4-42-22-220000000000000000000000000000000000000023−230000000000
χ4344-4-44004-4-4000000004-2-224-4-42-22-2200000000000000000000000000000000000000−23230000000000
χ4444-4-44004-4-400000000-244-4-222-4-22-22000000000000000000000000000000000000000023−2300000000
χ4544-4-44004-4-400000000-244-4-222-4-22-220000000000000000000000000000000000000000−232300000000
χ464-44-444i−4i-44-400004i−4i004-22-2-4-442-2-222−2i2i4i−4i00000000000000−2i2i000000000000000000000000000000
χ474-44-444i−4i-44-400004i−4i00-24-4422-2-4-2-2224i−4i−2i2i00000000000000−2i2i000000000000000000000000000000
χ484-44-444i−4i-44-400004i−4i00-2-22-222-2211-1-1−2i2i−2i2i00000000003-300i−i3i−3i0000000000000000000000000000
χ494-44-444i−4i-44-400004i−4i00-2-22-222-2211-1-1−2i2i−2i2i0000000000-3300i−i−3i3i0000000000000000000000000000
χ504-44-44−4i4i-44-40000−4i4i004-22-2-4-442-2-2222i−2i−4i4i000000000000002i−2i000000000000000000000000000000
χ514-44-44−4i4i-44-40000−4i4i00-24-4422-2-4-2-222−4i4i2i−2i000000000000002i−2i000000000000000000000000000000
χ524-44-44−4i4i-44-40000−4i4i00-2-22-222-2211-1-12i−2i2i−2i00000000003-300−ii−3i3i0000000000000000000000000000
χ534-44-44−4i4i-44-40000−4i4i00-2-22-222-2211-1-12i−2i2i−2i0000000000-3300−ii3i−3i0000000000000000000000000000
χ544-4-44400-4-440000000044-4-4-44-444-4-4400000000000000000000000000000000000000000000000000
χ554-4-44400-4-44000000004-222-44-4-2-222-200000000000000000000000000000000000000000000−2i32i30000
χ564-4-44400-4-44000000004-222-44-4-2-222-2000000000000000000000000000000000000000000002i3−2i30000
χ574-4-44400-4-4400000000-24-4-42-224-222-200000000000000000000000000000000000000000023−23000000
χ584-4-44400-4-4400000000-24-4-42-224-222-2000000000000000000000000000000000000000000−2323000000
χ596666-366-3-3-366-3-3-3-3-3-300000000000000002222-1-1-1-100000000002000002000-1-1-1-1-1-1000000000000
χ606666-366-3-3-366-3-3-3-3-3-30000000000000000-2-2-2-211110000000000-200000-2000111111000000000000
χ616666-366-3-3-3-6-633-3-33300000000000000002222-1-1-1-10000000000-200000-200011-1-111000000000000
χ626666-366-3-3-3-6-633-3-3330000000000000000-2-2-2-2111100000000002000002000-1-111-1-1000000000000
χ636666-3-6-6-3-3-36-6-3-33333000000000000000022-2-211110000000000200000-2000-1-1-1-111000000000000
χ646666-3-6-6-3-3-36-6-3-333330000000000000000-2-222-1-1-1-10000000000-20000020001111-1-1000000000000
χ656666-3-6-6-3-3-3-663333-3-3000000000000000022-2-211110000000000-200000200011-1-1-1-1000000000000
χ666666-3-6-6-3-3-3-663333-3-30000000000000000-2-222-1-1-1-10000000000200000-2000-1-11111000000000000
χ676-66-6-36i−6i3-3300−3i33i3−3i3i33−3300000000000000002-22i−2i−i−iii00000000000000000000−i3i3-113−3000000000000
χ686-66-6-36i−6i3-3300−3i33i3−3i3i33−330000000000000000-22−2i2iii−i−i00000000000000000000i3−i31-1−33000000000000
χ696-66-6-36i−6i3-33003i3−3i3−3i3i−333300000000000000002-22i−2i−i−iii00000000000000000000i3−i3-11−33000000000000
χ706-66-6-36i−6i3-33003i3−3i3−3i3i−33330000000000000000-22−2i2iii−i−i00000000000000000000−i3i31-13−3000000000000
χ716-66-6-3−6i6i3-3300−3i33i33i−3i−333300000000000000002-2−2i2iii−i−i00000000000000000000−i3i3-11−33000000000000
χ726-66-6-3−6i6i3-3300−3i33i33i−3i−33330000000000000000-222i−2i−i−iii00000000000000000000i3−i31-13−3000000000000
χ736-66-6-3−6i6i3-33003i3−3i33i−3i33−3300000000000000002-2−2i2iii−i−i00000000000000000000i3−i3-113−3000000000000
χ746-66-6-3−6i6i3-33003i3−3i33i−3i33−330000000000000000-222i−2i−i−iii00000000000000000000−i3i31-1−33000000000000
χ7588-8-88008-8-800000000-4-4-44-44442-22-200000000000000000000000000000000000000000000000000
χ768-8-88800-8-8800000000-4-4444-44-42-2-2200000000000000000000000000000000000000000000000000
χ771212-12-12-600-666000000000000000000000000000023−2323−2300000000000000000000000000000000000000
χ781212-12-12-600-6660000000000000000000000000000−2323−232300000000000000000000000000000000000000
χ7912-12-1212-60066-60000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ8012-12-1212-60066-600000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000

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