Finite Group Databasebeta

← Group #13165581

Character table — Group #13165581

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order12223666336666663366666644444266666666121212121212121212121212448812122424242444266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-1-1-111-1-1
χ311111111111111111111111111-11111111111111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1111-1-111
χ5111111111111111111111111-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1
χ6111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1-111
χ7111111111111111111111111-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-1
χ9222222222222222222222222002-2-20000000000022002200000000-2-20000-2-20000000
χ1022222222222222222222222200-2-2-200000000000-2-200-2-200000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1220222-1-122-1-1-1-1-1-1002200-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-122022-211-2-21111-1-1002200-1-1-1-100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-20222-1-122-1-1-1-11100-2-200111100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2022-211-2-211111100-2-20011110022-1-1-1-1-1-1000000000
χ152-22-222-2-22222-2-2-2-2222-22-2-2-20000000000000000000000000000−i2i200−i2−i2i2i22-200000−i2i2
χ162-22-222-2-22222-2-2-2-2222-22-2-2-20000000000000000000000000000−i2i200−i2−i2i2i2-2200000i2−i2
χ172-22-222-2-22222-2-2-2-2222-22-2-2-20000000000000000000000000000i2−i200i2i2−i2−i22-200000i2−i2
χ182-22-222-2-22222-2-2-2-2222-22-2-2-20000000000000000000000000000i2−i200i2i2−i2−i2-2200000−i2i2
χ192-2-222-2-2222-2-22-2-2222-22-22-2-2000-220000000000000000000002-200-220000000002-200
χ202-2-222-2-2222-2-22-2-2222-22-22-2-2000-22000000000000000000000-2200-22000000000-2200
χ212-2-222-2-2222-2-22-2-2222-22-22-2-22i−2i02-20000000002i−2i002i−2i002i2i−2i−2i00002-20000000000000
χ222-2-222-2-2222-2-22-2-2222-22-22-2-2−2i2i02-2000000000−2i2i00−2i2i00−2i−2i2i2i00002-20000000000000
χ232-2-22-111-122-2-22-2-22-1-11-11-1112i−2i02-20−i3i300−i3−i3i3i3−ii002i−2i00−i−iii0000-113−33−3000000000
χ242-2-22-111-122-2-22-2-22-1-11-11-1112i−2i02-20i3−i300i3i3−i3−i3−ii002i−2i00−i−iii0000-11−33−33000000000
χ252-2-22-111-122-2-22-2-22-1-11-11-111−2i2i02-20−i3i300−i3−i3i3i3i−i00−2i2i00ii−i−i0000-11−33−33000000000
χ262-2-22-111-122-2-22-2-22-1-11-11-111−2i2i02-20i3−i300i3i3−i3−i3i−i00−2i2i00ii−i−i0000-113−33−3000000000
χ27444444441-21-2-2-2111-211-2-2-212240000000000022-2-2-1-111-1-1-1-1220000000000000-1-100
χ28444444441-21-2-2-2111-211-2-2-2122-4000000000002222-1-1-1-1-1-1-1-1-2-200000000000001100
χ29444444441-21-2-2-2111-211-2-2-21-2-2400000000000-2-2-2-211111111-2-200000000000001100
χ30444444441-21-2-2-2111-211-2-2-21-2-2-400000000000-2-22211-1-11111220000000000000-1-100
χ3144444444-21-2111-2-2-21-2-2111-200400222-1-1-1-1-1-1001100-2-200000000000000002-1-10000
χ3244444444-21-2111-2-2-21-2-2111-200400-2-2-2111111001100-2-20000000000000000-2110000
χ3344444444-21-2111-2-2-21-2-2111-200-400222-1-1-1-1-1-100-1-100220000000000000000-2110000
χ3444444444-21-2111-2-2-21-2-2111-200-400-2-2-211111100-1-1002200000000000000002-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-44-44-444-4-4-444-444-4-4-4-444000000000000000000000000000000000000000000000
χ3744-4-44-44-4-212-1-11-22-2122-1-11-200000000−i3i3−i3i3−i3i3003-3000000000000000000000−i3i30000
χ3844-4-44-44-4-212-1-11-22-2122-1-11-200000000−i3i3−i3i3−i3i300-33000000000000000000000i3−i30000
χ3944-4-44-44-4-212-1-11-22-2122-1-11-200000000i3−i3i3−i3i3−i3003-3000000000000000000000i3−i30000
χ4044-4-44-44-4-212-1-11-22-2122-1-11-200000000i3−i3i3−i3i3−i300-33000000000000000000000−i3i30000
χ4144-4-4-22-2244-4-4-444-4-2-22222-2-200000000000000000000000000000000i6−i6−i6i6000000000
χ4244-4-4-22-2244-4-4-444-4-2-22222-2-200000000000000000000000000000000−i6i6i6−i6000000000
χ434-44-4-2-2224444-4-4-4-4-2-2-22-22220000000000000000000000000000−2i22i200i2i2−i2−i2000000000
χ444-44-4-2-2224444-4-4-4-4-2-2-22-222200000000000000000000000000002i2−2i200−i2−i2i2i2000000000
χ454-4-444-4-441-2-12-22-111-2-112-22-12i−2i0000000000002i−2i00−ii3i−3i−i−iii2-20000000000000-1100
χ464-4-444-4-441-2-12-22-111-2-112-22-12i−2i0000000000002i−2i00−ii−3i3i−i−iii-2200000000000001-100
χ474-4-444-4-441-2-12-22-111-2-112-22-1−2i2i000000000000−2i2i00i−i3i−3iii−i−i-2200000000000001-100
χ484-4-444-4-441-2-12-22-111-2-112-22-1−2i2i000000000000−2i2i00i−i−3i3iii−i−i2-20000000000000-1100
χ494-4-44-222-244-4-44-4-44-2-22-22-222000-4400000000000000000000000002-20000000000000
χ508888-4-4-4-42-42-4-4-422-12-1-1222-144000000000000-2-200-2-20011110000000000000000000
χ518888-4-4-4-42-42-4-4-422-12-1-1222-1-4-400000000000022002200-1-1-1-10000000000000000000
χ528888-4-4-4-4-42-4222-4-42-122-1-1-12000004-2-2-2-211110000000000000000000000000000000
χ538888-4-4-4-4-42-4222-4-42-122-1-1-1200000-42222-1-1-1-10000000000000000000000000000000
χ5488-8-88-88-82-4-244-42-22-4-2-244-42000000000000000000000000000000000000000000000
χ5588-8-8-44-442-4-244-42-2-1211-2-22-100000000000000000000003-33-30000000000000000000
χ5688-8-8-44-442-4-244-42-2-1211-2-22-10000000000000000000000-33-330000000000000000000
χ5788-8-8-44-44-424-2-22-442-1-2-211-1200000000−2i32i3i3−i3i3−i30000000000000000000000000000000
χ5888-8-8-44-44-424-2-22-442-1-2-211-12000000002i3−2i3−i3i3−i3i30000000000000000000000000000000
χ598-88-888-8-82-42-444-2-22-42-2-444-2000000000000000000000000000000000000000000000
χ608-88-888-8-8-42-42-2-244-42-442-2-24000000000000000000000000000000000000000000000
χ618-88-8-4-4442-42-444-2-2-12-112-2-2100000000000000000000003i−3i−3i3i0000000000000000000
χ628-88-8-4-4442-42-444-2-2-12-112-2-210000000000000000000000−3i3i3i−3i0000000000000000000
χ638-88-8-4-444-42-42-2-2442-12-2-111-200000000003-3-330000000000000000000000000000000
χ648-88-8-4-444-42-42-2-2442-12-2-111-20000000000-333-30000000000000000000000000000000
χ658-8-888-8-88-424-22-24-4-424-4-22-24000000000000000000000000000000000000000000000
χ668-8-88-444-42-4-24-44-22-121-1-22-214i−4i000000000000−2i2i00−2i2i00ii−i−i0000000000000000000
χ678-8-88-444-42-4-24-44-22-121-1-22-21−4i4i0000000000002i−2i002i−2i00−i−iii0000000000000000000
χ688-8-88-444-4-424-22-24-42-1-221-11-2000000−2i32i300i3i3−i3−i30000000000000000000000000000000
χ698-8-88-444-4-424-22-24-42-1-221-11-20000002i3−2i300−i3−i3i3i30000000000000000000000000000000

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