Finite Group Databasebeta

← Group #13148675

Character table — Group #13148675

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order12223446662466121212123366666636661212121222446666666612121212121222244444446666121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-11-11-1-111-1-1-1-111-1-1-1-1-1-111-1-1-111-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-11-1-1-111-1-1-1-1-1-1-1-111-1-1111-1-11
χ51111111111-1-1-1-111-1-1111111111111111111111111-1-1-1-1-1-111-1-1-11-1-11-11-11-1-1-11111-1-1111111-1-1-1-1
χ61111111111-1-1-1-111-1-1111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-11-11-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-111111-1-111-1-111-1-11-1-11
χ81111111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1111-111-111-1-1-1-11111-1-111-111-1
χ911111-1-11111-111-1-1-1-1111111111111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-11-1-11-111111-1-1-1-111-1-1-1-1-1-111
χ1011111-1-11111-111-1-1-1-1111111111111-1-1-1-111-1-111111111-1-1-1-1-1-11-111-1-11-11-111-1-1-1-1-1-1-1-1111111-1-1
χ1111111-1-11111-111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-11-111-1-1-1111111-1-1-1-1111-11-1
χ1211111-1-11111-111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-111111111-1-1-11-11
χ1311111-1-1111-11-1-1-1-111111111111111-1-1-1-111-1-11111-1-1-1-111-1-111-111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ1411111-1-1111-11-1-1-1-111111111111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-111111-1-1-1-1-1-111-1-11111-1-111
χ1511111-1-1111-11-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-11-1-1-1-111111111-1-1-1-1-1-111-11-11
χ1611111-1-1111-11-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1111-11-11-111-1-111-1-111-1-11111-1-11-11-1
χ172222222222222222222-12-12-12-1-1-1-1-122-1-1000000002-1-1-1-12-1-1-1-1020200220000-1-1000000-1-1000-1-10
χ182222222222222222222-12-12-12-1-1-1-1-122-1-1000000002-1-1-1-12-1-1-1-10-20-200-2-200001100000011000110
χ19222222222222222222-12-12-12-12-1-1-1-1-1-12200000000-12-1-12-1-1-1-1-1002020002200000000-1-100-1-1-100-1
χ20222222222222222222-12-12-12-12-1-1-1-1-1-12200000000-12-1-12-1-1-1-1-100-20-2000-2-2000000001100111001
χ212222222222-2-2-2-222-2-22-12-12-12-1-1-1-1-122-1-100000000-21111-2-1-111020-2002-20000-1-1000000-1-1000110
χ222222222222-2-2-2-222-2-22-12-12-12-1-1-1-1-122-1-100000000-21111-2-1-1110-20200-2200001100000011000-1-10
χ232222222222-2-2-2-222-2-2-12-12-12-12-1-1-1-1-1-122000000001-211-21-1-1110020-2000-2200000000110011-100-1
χ242222222222-2-2-2-222-2-2-12-12-12-12-1-1-1-1-1-122000000001-211-21-1-11100-2020002-200000000-1-100-1-11001
χ2522222-2-22222-222-2-2-2-22-12-12-12-1-1-1-1-1-2-211000000002-1-1-11-21111020-200-220000-1-1000000110001-10
χ2622222-2-22222-222-2-2-2-22-12-12-12-1-1-1-1-1-2-211000000002-1-1-11-211110-202002-2000011000000-1-1000-110
χ2722222-2-22222-222-2-2-2-2-12-12-12-12-1-1-1-111-2-200000000-12-1-1-2111110020-20002-2000000001100-1-1-1001
χ2822222-2-22222-222-2-2-2-2-12-12-12-12-1-1-1-111-2-200000000-12-1-1-21111100-202000-2200000000-1-10011100-1
χ2922222-2-2222-22-2-2-2-2222-12-12-12-1-1-1-1-1-2-21100000000-2111-1211-1-1020200-2-20000-1-100000011000-110
χ3022222-2-2222-22-2-2-2-2222-12-12-12-1-1-1-1-1-2-21100000000-2111-1211-1-10-20-20022000011000000-1-10001-10
χ3122222-2-2222-22-2-2-2-222-12-12-12-12-1-1-1-111-2-2000000001-2112-111-1-100202000-2-200000000-1-10011-1001
χ3222222-2-2222-22-2-2-2-222-12-12-12-12-1-1-1-111-2-2000000001-2112-111-1-100-20-200022000000001100-1-1100-1
χ3322-2-222i−2i2-2-200002i−2i0022-2-222-2-222-2-22i−2i2i−2i2-22i−2i22-2-20000002i−2i00000000000000002i−2i000000000000
χ3422-2-222i−2i2-2-200002i−2i0022-2-222-2-222-2-22i−2i2i−2i-22−2i2i-2-2220000002i−2i0000000000000000−2i2i000000000000
χ3522-2-22−2i2i2-2-20000−2i2i0022-2-222-2-222-2-2−2i2i−2i2i2-2−2i2i22-2-2000000−2i2i0000000000000000−2i2i000000000000
χ3622-2-22−2i2i2-2-20000−2i2i0022-2-222-2-222-2-2−2i2i−2i2i-222i−2i-2-222000000−2i2i00000000000000002i−2i000000000000
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
χ4144-4-444i−4i4-4-400004i−4i004-2-424-2-42-2-2224i−4i−2i2i00000000000000−2i2i000000000000000000000000000000
χ4244-4-444i−4i4-4-400004i−4i00-242-4-242-4-2-222−2i2i4i−4i00000000000000−2i2i000000000000000000000000000000
χ4344-4-444i−4i4-4-400004i−4i00-2-222-2-22211-1-1−2i2i−2i2i00000000003-300i−i3i−3i0000000000000000000000000000
χ4444-4-444i−4i4-4-400004i−4i00-2-222-2-22211-1-1−2i2i−2i2i0000000000-3300i−i−3i3i0000000000000000000000000000
χ4544-4-44−4i4i4-4-40000−4i4i004-2-424-2-42-2-222−4i4i2i−2i000000000000002i−2i000000000000000000000000000000
χ4644-4-44−4i4i4-4-40000−4i4i00-242-4-242-4-2-2222i−2i−4i4i000000000000002i−2i000000000000000000000000000000
χ4744-4-44−4i4i4-4-40000−4i4i00-2-222-2-22211-1-12i−2i2i−2i00000000003-300−ii−3i3i0000000000000000000000000000
χ4844-4-44−4i4i4-4-40000−4i4i00-2-222-2-22211-1-12i−2i2i−2i0000000000-3300−ii3i−3i0000000000000000000000000000
χ494-44-4400-44-400000000444-4-4-4-444-44-400000000000000000000000000000000000000000000000000
χ504-44-4400-44-4000000004-242-42-4-2-22-220000000000000000000000000000000000−2i32i300000000000000
χ514-44-4400-44-4000000004-242-42-4-2-22-2200000000000000000000000000000000002i3−2i300000000000000
χ524-44-4400-44-400000000-24-2-42-424-22-22000000000000000000000000000000000000000023−2300000000
χ534-44-4400-44-400000000-24-2-42-424-22-220000000000000000000000000000000000000000−232300000000
χ544-4-44400-4-440000000044-44-4-44-44-4-4400000000000000000000000000000000000000000000000000
χ554-4-44400-4-44000000004-2-4-2-4242-222-200000000000000000000000000000000000000000023−23000000
χ564-4-44400-4-44000000004-2-4-2-4242-222-2000000000000000000000000000000000000000000−2323000000
χ574-4-44400-4-4400000000-24242-4-2-4-222-200000000000000000000000000000000000000000000−2i32i30000
χ584-4-44400-4-4400000000-24242-4-2-4-222-2000000000000000000000000000000000000000000002i3−2i30000
χ596666-366-3-3-366-3-3-3-3-3-300000000000000002222-1-1-1-100000000002000020000-1-100-1-1-1-10000000000
χ606666-366-3-3-366-3-3-3-3-3-30000000000000000-2-2-2-211110000000000-20000-20000110011110000000000
χ616666-366-3-3-3-6-633-3-33300000000000000002222-1-1-1-10000000000-20000-200001100-1-1110000000000
χ626666-366-3-3-3-6-633-3-3330000000000000000-2-2-2-2111100000000002000020000-1-10011-1-10000000000
χ636666-3-6-6-3-3-36-6-3-33333000000000000000022-2-2-1-1-1-1000000000020000-20000-1-10011110000000000
χ646666-3-6-6-3-3-36-6-3-333330000000000000000-2-22211110000000000-20000200001100-1-1-1-10000000000
χ656666-3-6-6-3-3-3-663333-3-3000000000000000022-2-2-1-1-1-10000000000-2000020000110011-1-10000000000
χ666666-3-6-6-3-3-3-663333-3-30000000000000000-2-2221111000000000020000-20000-1-100-1-1110000000000
χ6766-6-6-36i−6i-33300−3i33i3−3i3i33−3300000000000000002-22i−2i-1-11100000000000000000000−i3i300−ii3−30000000000
χ6866-6-6-36i−6i-33300−3i33i3−3i3i33−330000000000000000-22−2i2i11-1-100000000000000000000i3−i300i−i−330000000000
χ6966-6-6-36i−6i-333003i3−3i3−3i3i−333300000000000000002-22i−2i-1-11100000000000000000000i3−i300−ii−330000000000
χ7066-6-6-36i−6i-333003i3−3i3−3i3i−33330000000000000000-22−2i2i11-1-100000000000000000000−i3i300i−i3−30000000000
χ7166-6-6-3−6i6i-33300−3i33i33i−3i−333300000000000000002-2−2i2i-1-11100000000000000000000−i3i300i−i−330000000000
χ7266-6-6-3−6i6i-33300−3i33i33i−3i−33330000000000000000-222i−2i11-1-100000000000000000000i3−i300−ii3−30000000000
χ7366-6-6-3−6i6i-333003i3−3i33i−3i33−3300000000000000002-2−2i2i-1-11100000000000000000000i3−i300i−i3−30000000000
χ7466-6-6-3−6i6i-333003i3−3i33i−3i33−330000000000000000-222i−2i11-1-100000000000000000000−i3i300−ii−330000000000
χ758-88-8800-88-800000000-4-4-44444-42-22-200000000000000000000000000000000000000000000000000
χ768-8-88800-8-8800000000-4-44-444-442-2-2200000000000000000000000000000000000000000000000000
χ7712-1212-12-6006-660000000000000000000000000000−2i32i3−2i32i300000000000000000000000000000000000000
χ7812-1212-12-6006-6600000000000000000000000000002i3−2i32i3−2i300000000000000000000000000000000000000
χ7912-12-1212-60066-60000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ8012-12-1212-60066-600000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000

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