Finite Group Databasebeta

← Group #13165515

Character table — Group #13165515

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order1222366633666666443366666622441212121212121212446666666612121212121212124444881212121212122424242444121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-11-1-1-1-11-1-1-1-11111-1-1
χ311111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-111
χ51111111111111111-1-1111111111111-1-1-1-11111111111111111-1-11111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ71111111111111111-1-111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-11-1-1-1-11-1-1-1-1-1-11111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1
χ91-11-11-1-11111-1-1-11-1i−i111-11-1-1-11-1i−iii−i−iii−i−i-111-11-111-1-1i−ii−iii−i−i1-1i−ii−i111-1-1-1ii−i−ii−ii−i1-1
χ101-11-11-1-11111-1-1-11-1i−i111-11-1-1-11-1−iiii−i−i−i−iii-111-11-111-1-1−iii−i−i−iii-11i−i−ii1-1-111-1−i−iiii−ii−i-11
χ111-11-11-1-11111-1-1-11-1i−i111-11-1-1-1-11i−iii−i−iii−i−i-11-11-11-1-111i−ii−iii−i−i1-1−ii−ii111-1-1-1−i−iiii−i−ii-11
χ121-11-11-1-11111-1-1-11-1i−i111-11-1-1-1-11−iiii−i−i−i−iii-11-11-11-1-111−iii−i−i−iii-11−iii−i1-1-111-1ii−i−ii−i−ii1-1
χ131-11-11-1-11111-1-1-11-1−ii111-11-1-1-11-1i−i−i−iiiii−i−i-111-11-111-1-1i−i−iiii−i−i-11−iii−i1-1-111-1ii−i−i−ii−ii-11
χ141-11-11-1-11111-1-1-11-1−ii111-11-1-1-11-1−ii−i−iii−i−iii-111-11-111-1-1−ii−ii−i−iii1-1−ii−ii111-1-1-1−i−iii−ii−ii1-1
χ151-11-11-1-11111-1-1-11-1−ii111-11-1-1-1-11i−i−i−iiiii−i−i-11-11-11-1-111i−i−iiii−i−i-11i−i−ii1-1-111-1−i−iii−iii−i1-1
χ161-11-11-1-11111-1-1-11-1−ii111-11-1-1-1-11−ii−i−iii−i−iii-11-11-11-1-111−ii−ii−i−iii1-1i−ii−i111-1-1-1ii−i−i−iii−i-11
χ1722222222222222222222222222000022220000-2-20000000000220000000000-20000-20000-2-20000
χ182222222222222222-2-2222222220000-2-2-2-20000-2-20000000000-2-20000000000-20000-20000220000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122220000222222-1-122-1-1-1-1-1-100-1-1-1-1000022-10000-1-1-1-1-1000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-20000-2-2-2-222-1-122-1-1-1-1110011110000-2-2-10000-11111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-222000022222211-2-21111-1-100-1-1-1-10000-2-2-10000-11111000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-22211-2-2111111001111000022-10000-1-1-1-1-1000000
χ232-22-22-2-22222-2-2-22-22i−2i222-22-2-2-200002i2i−2i−2i00002-200000000002i−2i0000000000-2000020000−2i2i0000
χ242-22-22-2-22222-2-2-22-2−2i2i222-22-2-2-20000−2i−2i2i2i00002-20000000000−2i2i0000000000-20000200002i−2i0000
χ252-22-2-111-1222-2-2-22-200-1-1-11-11112-22i−2i00002i2i−2i−2i-22-112-2-1-111−ii00−i−iii00002i−2i-100001−i−iii000000
χ262-22-2-111-1222-2-2-22-200-1-1-11-11112-2−2i2i0000−2i−2i2i2i-22-112-2-1-111i−i00ii−i−i0000−2i2i-100001ii−i−i000000
χ272-22-2-111-1222-2-2-22-200-1-1-11-1111-222i−2i00002i2i−2i−2i-221-1-2211-1-1−ii00−i−iii0000−2i2i-100001ii−i−i000000
χ282-22-2-111-1222-2-2-22-200-1-1-11-1111-22−2i2i0000−2i−2i2i2i-221-1-2211-1-1i−i00ii−i−i00002i−2i-100001−i−iii000000
χ29444444441-2-211-21-2441-211-2-2-2100221111-1-1-1-1000000000022-2-2-1-1-1-12200000-1-1-1-100000000000
χ30444444441-2-211-21-2441-211-2-2-2100-2-2111111110000000000-2-2-2-21111-2-200000111100000000000
χ31444444441-2-211-21-2-4-41-211-2-2-210022-1-1-1-1-1-1-1-100000000002222-1-1-1-1-2-200000111100000000000
χ32444444441-2-211-21-2-4-41-211-2-2-2100-2-2-1-1-1-111110000000000-2-22211112200000-1-1-1-100000000000
χ3344444444-211-2-21-2144-21-2-2111-22200-2-2-2-200000022-1-1-1-1-1-100110000002200000000000000-1-100
χ3444444444-211-2-21-2144-21-2-2111-2-2-200-2-2-2-2000000-2-21111110011000000-2-2000000000000001100
χ3544444444-211-2-21-21-4-4-21-2-2111-22200222200000022-1-1-1-1-1-100-1-1000000-2-2000000000000001100
χ3644444444-211-2-21-21-4-4-21-2-2111-2-2-2002222000000-2-211111100-1-10000002200000000000000-1-100
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000002000020000000000
χ3844-4-444-4-41-221-1-2-12001-2-1122-2-100003-33-33−33−3000000000000003−33−300000003−33−300000000000
χ3944-4-444-4-41-221-1-2-12001-2-1122-2-100003-33-3−33−3300000000000000−33−330000000−33−3300000000000
χ4044-4-444-4-41-221-1-2-12001-2-1122-2-10000-33-333−33−3000000000000003−33−30000000−33−3300000000000
χ4144-4-444-4-41-221-1-2-12001-2-1122-2-10000-33-33−33−3300000000000000−33−3300000003−33−300000000000
χ4244-4-444-4-444-44-44-4-40044-44-4-44-40000000000000000000000000000000000000000000000000000
χ4344-4-4-2-22244-44-44-4-400-2-22-222-220000000000000000000000000000000000000000006−66−6000000
χ4444-4-4-2-22244-44-44-4-400-2-22-222-22000000000000000000000000000000000000000000−66−66000000
χ454-44-44-4-441-2-2-1-12124i−4i1-21-1-222-1002i−2iii−i−i−i−iii00000000002i−2i−2i2i−i−iii2-200000-1-11100000000000
χ464-44-44-4-441-2-2-1-12124i−4i1-21-1-222-100−2i2iii−i−iii−i−i0000000000−2i2i−2i2iii−i−i-220000011-1-100000000000
χ474-44-44-4-441-2-2-1-1212−4i4i1-21-1-222-1002i−2i−i−iii−i−iii00000000002i−2i2i−2i−i−iii-220000011-1-100000000000
χ484-44-44-4-441-2-2-1-1212−4i4i1-21-1-222-100−2i2i−i−iiiii−i−i0000000000−2i2i2i−2iii−i−i2-200000-1-11100000000000
χ494-44-44-4-44-21122-1-2-14i−4i-21-221-1-122-200−2i−2i2i2i0000002-2-11-1-11100i−i0000002i−2i00000000000000−ii00
χ504-44-44-4-44-21122-1-2-14i−4i-21-221-1-12-2200−2i−2i2i2i000000-221-111-1-100i−i000000−2i2i00000000000000i−i00
χ514-44-44-4-44-21122-1-2-1−4i4i-21-221-1-122-2002i2i−2i−2i0000002-2-11-1-11100−ii000000−2i2i00000000000000i−i00
χ524-44-44-4-44-21122-1-2-1−4i4i-21-221-1-12-22002i2i−2i−2i000000-221-111-1-100−ii0000002i−2i00000000000000−ii00
χ534-44-4-222-2444-4-4-44-400-2-2-22-22220000000000004-4000000000000000000000020000-20000000000
χ544-4-444-44-41-22-112-1-2001-2-1-12-22100003i−3i−3i3i−i3i3i3−i300000000000000−i3i3i3−i30000000−333−300000000000
χ554-4-444-44-41-22-112-1-2001-2-1-12-22100003i−3i−3i3ii3−i3−i3i300000000000000i3−i3−i3i300000003−3−3300000000000
χ564-4-444-44-41-22-112-1-2001-2-1-12-2210000−3i3i3i−3i−i3i3i3−i300000000000000−i3i3i3−i300000003−3−3300000000000
χ574-4-444-44-41-22-112-1-2001-2-1-12-2210000−3i3i3i−3ii3−i3−i3i300000000000000i3−i3−i3i30000000−333−300000000000
χ584-4-444-44-444-4-44-4-440044-4-4-44-440000000000000000000000000000000000000000000000000000
χ594-4-44-22-2244-4-44-4-4400-2-2222-22-2000000000000000000000000000000000000000000i6−i6−i6i6000000
χ604-4-44-22-2244-4-44-4-4400-2-2222-22-2000000000000000000000000000000000000000000−i6i6i6−i6000000
χ618888-4-4-4-42-4-422-42-400-12-1-1222-100440000-2-2-2-20000000000-2-20011110000000000000000000000
χ628888-4-4-4-42-4-422-42-400-12-1-1222-100-4-40000222200000000002200-1-1-1-10000000000000000000000
χ638888-4-4-4-4-422-4-42-42002-122-1-1-1244000000000000-2-2-2-21111000000000000000000000000000000
χ648888-4-4-4-4-422-4-42-42002-122-1-1-12-4-40000000000002222-1-1-1-1000000000000000000000000000000
χ6588-8-888-8-8-42-2-4424-200-424-4-2-2240000000000000000000000000000000000000000000000000000
χ6688-8-8-4-4442-442-2-4-2400-121-1-2-2210000000023−2323−2300000000000000−33−330000000000000000000000
χ6788-8-8-4-4442-442-2-4-2400-121-1-2-22100000000−2323−2323000000000000003−33−30000000000000000000000
χ6888-8-8-4-444-42-2-4424-2002-1-2211-1-20000000000000000003-33-3000000000000000000000000000000
χ6988-8-8-4-444-42-2-4424-2002-1-2211-1-2000000000000000000-33-33000000000000000000000000000000
χ708-88-8-444-42-4-4-2-242400-12-112-2-21004i−4i0000−2i−2i2i2i0000000000−2i2i00ii−i−i0000000000000000000000
χ718-88-8-444-42-4-4-2-242400-12-112-2-2100−4i4i00002i2i−2i−2i00000000002i−2i00−i−iii0000000000000000000000
χ728-88-8-444-4-42244-2-4-2002-12-2-111-24-4000000000000-22-2211-1-1000000000000000000000000000000
χ738-88-8-444-4-42244-2-4-2002-12-2-111-2-440000000000002-22-2-1-111000000000000000000000000000000
χ748-8-888-88-8-42-24-4-24200-4244-22-2-40000000000000000000000000000000000000000000000000000
χ758-8-88-44-442-44-224-2-400-1211-22-2-100000000−2i32i32i3−2i300000000000000i3−i3−i3i30000000000000000000000
χ768-8-88-44-442-44-224-2-400-1211-22-2-1000000002i3−2i3−2i32i300000000000000−i3i3i3−i30000000000000000000000
χ778-8-88-44-44-42-24-4-242002-1-2-21-1120000000000000000003-3-33000000000000000000000000000000
χ788-8-88-44-44-42-24-4-242002-1-2-21-112000000000000000000-333-3000000000000000000000000000000

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