Finite Group Databasebeta

← Group #13165684

Character table — Group #13165684

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order1222366633666666336666664444426666666612121212121212121212121244881212242424242241212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-1-1-111-1-1
χ31111111111111111111111111-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111
χ5111111111111111111111111-1111111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-11111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111-1-111
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
χ9222222222222222222222222200-2-20000000000022220000000000-2-20000-2-20000000
χ10222222222222222222222222-200-2-200000000000-2-2-2-20000000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1022222-1-122-1-1-1-1-1-1000022-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-102222-211-2-21111-1-1000022-1-1-1-100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-2222-1-122-1-1-1-1110000-2-2111100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-222-211-2-21111110000-2-211110022-1-1-1-1-1-1000000000
χ1522-2-22-2-2222-2-222-2-2222-22-2-2-20002-20000000000000000000002i−2i00-220000000002i−2i00
χ1622-2-22-2-2222-2-222-2-2222-22-2-2-20002-2000000000000000000000−2i2i00-22000000000−2i2i00
χ1722-2-22-2-2222-2-222-2-2222-22-2-2-202i−2i-220000000002i−2i00002i−2i2i2i−2i−2i00002-20000000000000
χ1822-2-22-2-2222-2-222-2-2222-22-2-2-20−2i2i-22000000000−2i2i0000−2i2i−2i−2i2i2i00002-20000000000000
χ1922-2-2-111-122-2-222-2-2-1-1-11-111102i−2i-220−i3i300−i3−i3i3i3−ii00002i−2i−i−iii0000-1133−3−3000000000
χ2022-2-2-111-122-2-222-2-2-1-1-11-111102i−2i-220i3−i300i3i3−i3−i3−ii00002i−2i−i−iii0000-11−3−333000000000
χ2122-2-2-111-122-2-222-2-2-1-1-11-11110−2i2i-220−i3i300−i3−i3i3i3i−i0000−2i2iii−i−i0000-11−3−333000000000
χ2222-2-2-111-122-2-222-2-2-1-1-11-11110−2i2i-220i3−i300i3i3−i3−i3i−i0000−2i2iii−i−i0000-1133−3−3000000000
χ232-22-222-2-2222-2-2-22-222-22-22-2-20000000000000000000000000000−i2i200−i2i2−i2i22-200000−i2i2
χ242-22-222-2-2222-2-2-22-222-22-22-2-20000000000000000000000000000−i2i200−i2i2−i2i2-2200000i2−i2
χ252-22-222-2-2222-2-2-22-222-22-22-2-20000000000000000000000000000i2−i200i2−i2i2−i22-200000i2−i2
χ262-22-222-2-2222-2-2-22-222-22-22-2-20000000000000000000000000000i2−i200i2−i2i2−i2-2200000−i2i2
χ27444444441-21-21-2-211-211-2-2-21422000000000002211-2-2-1-1-1-1-1-1220000000000000-1-100
χ28444444441-21-21-2-211-211-2-2-214-2-200000000000-2-211-2-2111111-2-200000000000001100
χ29444444441-21-21-2-211-211-2-2-21-4220000000000022-1-122-1-1-1-1-1-1-2-200000000000001100
χ30444444441-21-21-2-211-211-2-2-21-4-2-200000000000-2-2-1-122111111220000000000000-1-100
χ3144444444-21-21-211-2-21-2-2111-240000222-1-1-1-1-1-100-2-2110000000000000000002-1-10000
χ3244444444-21-21-211-2-21-2-2111-240000-2-2-211111100-2-211000000000000000000-2110000
χ3344444444-21-21-211-2-21-2-2111-2-40000222-1-1-1-1-1-10022-1-1000000000000000000-2110000
χ3444444444-21-21-211-2-21-2-2111-2-40000-2-2-21111110022-1-10000000000000000002-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-44-4-441-2-121-22-11-21-1-222-102i−2i000000000002i−2i3-300−ii−i−iii2i−2i0000000000000−ii00
χ3744-4-44-4-441-2-121-22-11-21-1-222-102i−2i000000000002i−2i-3300−ii−i−iii−2i2i0000000000000i−i00
χ3844-4-44-4-441-2-121-22-11-21-1-222-10−2i2i00000000000−2i2i3-300i−iii−i−i−2i2i0000000000000i−i00
χ3944-4-44-4-441-2-121-22-11-21-1-222-10−2i2i00000000000−2i2i-3300i−iii−i−i2i−2i0000000000000−ii00
χ4044-4-4-222-244-4-444-4-4-2-2-22-22220004-400000000000000000000000002-20000000000000
χ414-44-4-2-222444-4-4-44-4-2-22-22-2220000000000000000000000000000−2i22i200i2−i2i2−i2000000000
χ424-44-4-2-222444-4-4-44-4-2-22-22-22200000000000000000000000000002i2−2i200−i2i2−i2i2000000000
χ434-4-444-44-444-44-4-4-4444-4-4-4-444000000000000000000000000000000000000000000000
χ444-4-444-44-4-21212-1-1-2-2122-1-11-200000000−i3i3−i3i3−i3i300003i−3i00000000000000000003−30000
χ454-4-444-44-4-21212-1-1-2-2122-1-11-200000000−i3i3−i3i3−i3i30000−3i3i0000000000000000000−330000
χ464-4-444-44-4-21212-1-1-2-2122-1-11-200000000i3−i3i3−i3i3−i300003i−3i0000000000000000000−330000
χ474-4-444-44-4-21212-1-1-2-2122-1-11-200000000i3−i3i3−i3i3−i30000−3i3i00000000000000000003−30000
χ484-4-44-22-2244-44-4-4-44-2-22222-2-200000000000000000000000000000000i6−i6−i6i6000000000
χ494-4-44-22-2244-44-4-4-44-2-22222-2-200000000000000000000000000000000−i6i6i6−i6000000000
χ508888-4-4-4-42-42-42-4-42-12-1-1222-104400000000000-2-20000-2-211110000000000000000000
χ518888-4-4-4-42-42-42-4-42-12-1-1222-10-4-40000000000022000022-1-1-1-10000000000000000000
χ528888-4-4-4-4-42-42-422-42-122-1-1-12000004-2-2-2-211110000000000000000000000000000000
χ538888-4-4-4-4-42-42-422-42-122-1-1-1200000-42222-1-1-1-10000000000000000000000000000000
χ5488-8-88-8-88-424-2-42-24-42-442-2-24000000000000000000000000000000000000000000000
χ5588-8-8-444-42-4-242-44-2-12-112-2-2104i−4i00000000000−2i2i0000−2i2iii−i−i0000000000000000000
χ5688-8-8-444-42-4-242-44-2-12-112-2-210−4i4i000000000002i−2i00002i−2i−i−iii0000000000000000000
χ5788-8-8-444-4-424-2-42-242-12-2-111-2000000−2i32i300i3i3−i3−i30000000000000000000000000000000
χ5888-8-8-444-4-424-2-42-242-12-2-111-20000002i3−2i300−i3−i3i3i30000000000000000000000000000000
χ598-88-888-8-82-424-24-4-22-4-224-44-2000000000000000000000000000000000000000000000
χ608-88-888-8-8-42-4-24-224-424-4-22-24000000000000000000000000000000000000000000000
χ618-88-8-4-4442-424-24-4-2-121-1-22-2100000000000000000000003i−3i3i−3i0000000000000000000
χ628-88-8-4-4442-424-24-4-2-121-1-22-210000000000000000000000−3i3i−3i3i0000000000000000000
χ638-88-8-4-444-42-4-24-2242-1-221-11-200000000003-3-330000000000000000000000000000000
χ648-88-8-4-444-42-4-24-2242-1-221-11-20000000000-333-30000000000000000000000000000000
χ658-8-888-88-82-4-2-4-24422-4-2-244-42000000000000000000000000000000000000000000000
χ668-8-88-44-442-4-2-4-2442-1211-2-22-100000000000000000000003-3-330000000000000000000
χ678-8-88-44-442-4-2-4-2442-1211-2-22-10000000000000000000000-333-30000000000000000000
χ688-8-88-44-44-42424-2-2-42-1-2-211-1200000000−2i32i3i3−i3i3−i30000000000000000000000000000000
χ698-8-88-44-44-42424-2-2-42-1-2-211-12000000002i3−2i3−i3i3−i3i30000000000000000000000000000000

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