Finite Group Databasebeta

← Group #13166030

Character table — Group #13166030

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222444466666666888888888888121212121616161616161616161616162424242424242424242424242424363636363636363636727272108108216
order122233666666366644441212121233366666666612121212333666666666121212121212121212121212121248812122424242441212882
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-1
χ41111111111111111-1-111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ5222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1200220000000000
χ62222222222222222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122111111111111-200-2-20000000000
χ722222-122-1-1-12-1-1-1-12222-1-1-1-12-1-122-1-1-1-12-1-1-1-1222-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1200-1-10000000000
χ822222-122-1-1-12-1-1-1-12222-1-1-1-1-12-1-1-122-1-1-12-1-1-122-12-1-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1200-1-10000000000
χ922222-122-1-1-12-1-1-1-12222-1-1-1-1-1-12-1-1-1-122-1-12-1-122-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12222200-1-10000000000
χ1022222-122-1-1-12-1-1-1-1-2-22211112-1-122-1-1-1-12-1-1-1-1222-1-1222-1-1-1-1-1-1-1-1-2-2-2-211111111-200110000000000
χ1122222-122-1-1-12-1-1-1-1-2-2221111-12-1-1-122-1-1-12-1-1-122-12-1-1-1-1222-1-1-1-1-11111-2-2-2-21111-200110000000000
χ1222222-122-1-1-12-1-1-1-1-2-2221111-1-12-1-1-1-122-1-12-1-122-1-12-1-1-1-1-1-1222-1-111111111-2-2-2-2-200110000000000
χ132222-12-1-1222-1-1-1-1-10022000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000002200-1-1-1-12-1-1000
χ142222-12-1-1222-1-1-1-1-10022000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000-2-2001111-211000
χ152-22-2222-2-2-22-222-2-22i−2i002i2i−2i−2i-1-1-11-11-11-11110000-1-1-111-111-111-100ii−i−iii−i−iii−i−i02−20022−2−2000−i2i20
χ162-22-2222-2-2-22-222-2-22i−2i002i2i−2i−2i-1-1-11-11-11-11110000-1-1-111-111-111-100ii−i−iii−i−iii−i−i0−2200−2−222000i2−i20
χ172-22-2222-2-2-22-222-2-2−2i2i00−2i−2i2i2i-1-1-11-11-11-11110000-1-1-111-111-111-100−i−iii−i−iii−i−iii02−20022−2−2000i2−i20
χ182-22-2222-2-2-22-222-2-2−2i2i00−2i−2i2i2i-1-1-11-11-11-11110000-1-1-111-111-111-100−i−iii−i−iii−i−iii0−2200−2−222000−i2i20
χ192-2-2222-2-22-2-222-2-2200-2200002222-22-22-2-2-2-22-2-222222-2-22-2-22-2-22-2000000000000000000000000000
χ202-2-2222-2-22-2-222-2-2200-220000-1-1-1-11-11-111112-2-22-1-1-1-111-111-1112-23−33−33−33−33−33−3000000000000000
χ212-2-2222-2-22-2-222-2-2200-220000-1-1-1-11-11-111112-2-22-1-1-1-111-111-1112-2−33−33−33−33−33−33000000000000000
χ222-2-222-1-2-2-1112-111-100-223−33−32-1-12-2-11-11-211-11-222-1-12-2-2-111-111-1100003−33−3−33−330003−30000000000
χ232-2-222-1-2-2-1112-111-100-223−33−3-12-1-112-2-111-21-11-22-12-1-1112-2-2-111-11−33−3300003−33−30003−30000000000
χ242-2-222-1-2-2-1112-111-100-223−33−3-1-12-11-112-211-2-11-22-1-12-111-1112-2-2-113−33−3−33−3300000003−30000000000
χ252-2-222-1-2-2-1112-111-100-22−33−332-1-12-2-11-11-211-11-222-1-12-2-2-111-111-110000−33−333−33−3000−330000000000
χ262-2-222-1-2-2-1112-111-100-22−33−33-12-1-112-2-111-21-11-22-12-1-1112-2-2-111-113−33−30000−33−33000−330000000000
χ272-2-222-1-2-2-1112-111-100-22−33−33-1-12-11-112-211-2-11-22-1-12-111-1112-2-2-11−33−333−33−30000000−330000000000
χ282-2-22-12112-2-2-1-111-100-2200002222-22-22-2-2-2-22-21-1-1-1-1-111-111-111-1100000000000000000−i3i3−i3i30−i3i3000
χ292-2-22-12112-2-2-1-111-100-2200002222-22-22-2-2-2-22-21-1-1-1-1-111-111-111-1100000000000000000i3−i3i3−i30i3−i3000
χ30333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-1000000000000-111-1-11111-1-1-111-1
χ31333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-1000000000000-1-1-1-1-1-1-1-1-1111-1-11
χ323333333333333333-3-3-1-1-3-3-3-3000000000000-1-1-1-1000000000000-1-1000000000000111111111-1-1-1-1-11
χ333333333333333333-3-3-1-1-3-3-3-3000000000000-1-1-1-1000000000000-1-10000000000001-1-111-1-1-1-111111-1
χ344444-24-2-2444-2-2-2-2-200440000-2-2-2-2-2-2-2-2-2-2-2-244-2-2111111111111-2-2000000000000000000000000000
χ354444-2-2-2-2-2-2-2-21111004400004-2-244-2-2-2-24-2-2-2-2-2-2-211-2-2-211111111000000000000000000000000000
χ364444-2-2-2-2-2-2-2-2111100440000-24-2-2-244-2-2-24-2-2-2-2-21-21111-2-2-211111000000000000000000000000000
χ374444-2-2-2-2-2-2-2-2111100440000-2-24-2-2-2-244-2-24-2-2-2-211-2111111-2-2-211000000000000000000000000000
χ3844-4-444-44-44-4-44-44-400000000111-1-1-1-1-1-11110000111-11-1-11-1-11-100−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000000
χ3944-4-444-44-44-4-44-44-400000000111-1-1-1-1-1-11110000111-11-1-11-1-11-100i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000000
χ4044-4-444-44-44-4-44-44-400000000-2-2-2222222-2-2-20000-2-2-22-222-222-2200000000000000000000000000000
χ4144-4-44-2-442-22-4-22-220000−2i32i32i3−2i311-2-1-1-1-12211-2000011-2-11-1-11-12-2200−i3i3i3−i3i3−i3−i3i30000000000000000000
χ4244-4-44-2-442-22-4-22-220000−2i32i32i3−2i31-21-1-122-1-11-2100001-21-11-12-22-11-100i3−i3−i3i30000−i3i3i3−i3000000000000000
χ4344-4-44-2-442-22-4-22-220000−2i32i32i3−2i3-21122-1-1-1-1-2110000-2112-22-11-1-11-1000000−i3i3i3−i3i3−i3−i3i3000000000000000
χ4444-4-44-2-442-22-4-22-2200002i3−2i3−2i32i311-2-1-1-1-12211-2000011-2-11-1-11-12-2200i3−i3−i3i3−i3i3i3−i30000000000000000000
χ4544-4-44-2-442-22-4-22-2200002i3−2i3−2i32i31-21-1-122-1-11-2100001-21-11-12-22-11-100−i3i3i3−i30000i3−i3−i3i3000000000000000
χ4644-4-44-2-442-22-4-22-2200002i3−2i3−2i32i3-21122-1-1-1-1-2110000-2112-22-11-1-11-1000000i3−i3−i3i3−i3i3i3−i3000000000000000
χ4744-4-4-242-2-44-42-22-2200000000-2-2-2222222-2-2-20000111-11-1-11-1-11-10000000000000000000i6−i6−i6i6000000
χ4844-4-4-242-2-44-42-22-2200000000-2-2-2222222-2-2-20000111-11-1-11-1-11-10000000000000000000−i6i6i6−i6000000
χ494-44-4444-4-4-44-444-4-44i−4i004i4i−4i−4i111-11-11-11-1-1-10000111-1-11-1-11-1-1100−i−iii−i−iii−i−iii000000000000000
χ504-44-4444-4-4-44-444-4-4−4i4i00−4i−4i4i4i111-11-11-11-1-1-10000111-1-11-1-11-1-1100ii−i−iii−i−iii−i−i000000000000000
χ514-44-44-24-422-2-4-2-2224i−4i00−2i−2i2i2i11-2-11-112-2-1-12000011-2-1-11-1-1122-200−i−iii−i−iii2i2i−2i−2i000000000000000
χ524-44-44-24-422-2-4-2-2224i−4i00−2i−2i2i2i1-21-112-2-11-12-100001-21-1-1122-2-1-1100−i−iii2i2i−2i−2i−i−iii000000000000000
χ534-44-44-24-422-2-4-2-2224i−4i00−2i−2i2i2i-2112-2-11-112-1-10000-21122-2-1-11-1-11002i2i−2i−2i−i−iii−i−iii000000000000000
χ544-44-44-24-422-2-4-2-222−4i4i002i2i−2i−2i11-2-11-112-2-1-12000011-2-1-11-1-1122-200ii−i−iii−i−i−2i−2i2i2i000000000000000
χ554-44-44-24-422-2-4-2-222−4i4i002i2i−2i−2i1-21-112-2-11-12-100001-21-1-1122-2-1-1100ii−i−i−2i−2i2i2iii−i−i000000000000000
χ564-44-44-24-422-2-4-2-222−4i4i002i2i−2i−2i-2112-2-11-112-1-10000-21122-2-1-11-1-1100−2i−2i2i2iii−i−iii−i−i000000000000000
χ574-44-4-24-22-4-442-2-22200000000-2-2-22-22-22-22220000111-1-11-1-11-1-1100000000000000022−2200−2−222000000
χ584-44-4-24-22-4-442-2-22200000000-2-2-22-22-22-22220000111-1-11-1-11-1-11000000000000000−22220022−2−2000000
χ594-4-44-24224-4-4-2-222-200-440000-2-2-2-22-22-222224-42-21111-1-11-1-11-1-1-22000000000000000000000000000
χ604-4-44-2-222-222-21-1-1100-4400004-2-24-4-22-22-422-222-2-211-2221-1-11-1-11-1000000000000000000000000000
χ614-4-44-2-222-222-21-1-1100-440000-24-2-224-4-222-42-222-21-211-1-1-2221-1-11-1000000000000000000000000000
χ624-4-44-2-222-222-21-1-1100-440000-2-24-22-224-422-4-222-211-21-1-11-1-1-2221-1000000000000000000000000000
χ6366666-366-3-3-36-3-3-3-366-2-2-3-3-3-300000000000011-2-200000000000011000000000000-200110000000000
χ6466666-366-3-3-36-3-3-3-3-6-6-2-2333300000000000011-2-200000000000011000000000000200-1-10000000000
χ656666-36-3-3666-3-3-3-3-300-2-20000000000000000-2-2110000000000001100000000000002200-1-1-1-1-211000
χ666666-36-3-3666-3-3-3-3-300-2-20000000000000000-2-211000000000000110000000000000-2-20011112-1-1000
χ676-6-6666-6-66-6-666-6-66002-20000000000000000-222-2000000000000-22000000000000000000000000000
χ686-6-666-3-6-6-3336-333-3002-233−3333−330000000000001-12-20000000000001-1000000000000000−330000000000
χ696-6-666-3-6-6-3336-333-3002-2−3333−33330000000000001-12-20000000000001-10000000000000003−30000000000
χ706-6-66-36336-6-6-3-333-3002-20000000000000000-22-110000000000001-100000000000000000−i3i3−i3i30i3−i3000
χ716-6-66-36336-6-6-3-333-3002-20000000000000000-22-110000000000001-100000000000000000i3−i3i3−i30−i3i3000
χ7288-8-8-484-4-88-84-44-4400000000222-2-2-2-2-2-22220000-1-1-11-111-111-1100000000000000000000000000000
χ7388-8-8-4-44-44-4442-22-20000000022-4-2-2-2-24422-40000-1-121-111-11-22-200000000000000000000000000000
χ7488-8-8-4-44-44-4442-22-2000000002-42-2-244-2-22-420000-12-11-11-22-21-1100000000000000000000000000000
χ7588-8-8-4-44-44-4442-22-200000000-42244-2-2-2-2-42200002-1-1-22-21-111-1100000000000000000000000000000
χ768-88-8-48-44-8-884-4-44400000000222-22-22-22-2-2-20000-1-1-111-111-111-100000000000000000000000000000
χ778-88-8-4-4-4444-4422-2-20000000022-4-22-224-4-2-240000-1-1211-111-1-2-2200000000000000000000000000000
χ788-88-8-4-4-4444-4422-2-2000000002-42-224-4-22-24-20000-12-111-1-2-2211-100000000000000000000000000000
χ798-88-8-4-4-4444-4422-2-200000000-4224-4-22-224-2-200002-1-1-2-2211-111-100000000000000000000000000000
χ8012121212-6-6-6-6-6-6-6-6333300-4-400000000000000002222000000000000-1-1000000000000000000000000000
χ8112-12-1212-6-666-666-63-3-33004-400000000000000002-2-22000000000000-11000000000000000000000000000

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