Finite Group Databasebeta

← Group #13180508

Character table — Group #13180508

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444466888888881212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363654547272108108
order124436121233661212121224336612121212224466661212121224666666661212121212121212224466688121212242424242461288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-11-111111111111-11-111-1-11-11-111-1-11-11-1111-1-1111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-11-1111-1-111-1-111-1111-1-111-1111-1-111-11-111-1-1-1-1-1-11-1-1-1-11111-1-1
χ411111111111111111111111111-1-1-1-111-1-111-1-111-1-11-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11-1-111-1-11111111-1-111
χ51111111111111111-1-1111111111111-1-111-1-1111111-11111111-111111-1-1-1-11-1-111-1-111111-1-1-1-1-1-1
χ61111111111111111-1-1111111111-11-1-1-111-1-111111-1-1-111-1-11-1-1-111-1-1-11-111-1-1-1-1-1-11-1-1-1-1-1-11111
χ71111111111111111-1-111111111-11-11-1-1-1-1-1-1-1-111-11-11-1-111-11-11-1-1111-11-1111-1-1111-1-1-1-1-1-1-1-111
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
χ911-1-111-1-11111-1-1-1-11-11111-1-1-1-111-1-11111-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-11-1111-1-1-1111-1-1-11-111-1
χ1011-1-111-1-11111-1-1-1-11-11111-1-1-1-11-1-111111-1-1-1-1-111-11-111-1-1-11-11-1-11111-1-1-111-11-1-11-1-111-111-1-11
χ1111-1-111-1-11111-1-1-1-11-11111-1-1-1-1-111-111-1-1-1-111-11-1111-1-1111-1-1-111-1-1-1-111-1-1-1-11111-1-111-11-11-11
χ1211-1-111-1-11111-1-1-1-11-11111-1-1-1-1-1-11111-1-1-1-111-11-1-11-1-1-1-1-111-111111-111-1-1-1-11-111111-1-1-111-11-1
χ1311-1-111-1-11111-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1111-111111-1-11-1-1-1-1-1-111-1-1-1-11-111111-1-11-11-1-11
χ1411-1-111-1-11111-1-1-1-1-111111-1-1-1-11-1-11-1-11111-1-1-111-1-1-111-1-1-1111-1-111-1-111-1-1-1-11111-1-1111-1-111-1
χ1511-1-111-1-11111-1-1-1-1-111111-1-1-1-1-111-1-1-1-1-11111-11-11-11-1-1111-11-111-1-111-1-1-111-11-1-11-1-1111-11-11-1
χ1611-1-111-1-11111-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111-11-1-1-1-1-1-1-1-1111111111-1-11-1111-1-1-1111-1-11-1-11-11
χ1722222222222222222222222222000022002200-2-200200000002000000000-2000000-20000-2-20000
χ182222222222222222-2-2222222220000-2-200-2-200-2-200-20000000-2000000000-2000000-20000220000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-122220022002222-1-102-1-1-1-1-1-102-1-1-1-10000-1002200-1-1-1-1-1000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-12-22-20022002222-110-2-1-111-110-2-1-1110000-100-2-200-11111000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-22-2200-2-200-2-2221-10211-1-11-10211-1-10000-100-2-200-11111000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-200-2-200-2-222110-21111110-211110000-1002200-1-1-1-1-1000000
χ2322-2-222-2-22222-2-2-2-22-22222-2-2-2-200002200-2-2002-20020000000-20000000002000000-200002-20000
χ2422-2-222-2-22222-2-2-2-2-222222-2-2-2-20000-2-20022002-200-2000000020000000002000000-20000-220000
χ2522-2-2-1-1112222-2-2-2-200-1-1-1-1111122-2-2002200-2-2-22-1-102-1-1-1-1110-2111100001002-200-1-1-111000000
χ2622-2-2-1-1112222-2-2-2-200-1-1-1-111112-2-22002200-2-2-22-110-2-1-1111-10211-1-10000100-2200-111-1-1000000
χ2722-2-2-1-1112222-2-2-2-200-1-1-1-11111-222-200-2-20022-221-10211-1-1-110-2-1-1110000100-2200-111-1-1000000
χ2822-2-2-1-1112222-2-2-2-200-1-1-1-11111-2-22200-2-20022-22110-21111-1-102-1-1-1-100001002-200-1-1-111000000
χ29444444441-21-211-2-2441-21-211-2-20202-2-200-2-20000021-100-1-1021-100-1-1020200000000000000-1-100
χ30444444441-21-211-2-2441-21-211-2-20-20-2-2-200-2-200000-21100110-21100110-20-2000000000000001100
χ31444444441-21-211-2-2-4-41-21-211-2-20202220022000002-1-100-1-102-1-100-1-10-20-2000000000000001100
χ32444444441-21-211-2-2-4-41-21-211-2-20-20-222002200000-2-1100110-2-110011020200000000000000-1-100
χ3344444444-21-21-2-21144-21-21-2-211202011-1-111-1-10020-20-1-10020-20-1-10020200-1-100-1-100000000000
χ3444444444-21-21-2-21144-21-21-2-211-20-201111111100-20-201100-20-201100-20-20011001100000000000
χ3544444444-21-21-2-211-4-4-21-21-2-2112020-1-1-1-1-1-1-1-1002020-1-1002020-1-100-20-20011001100000000000
χ3644444444-21-21-2-211-4-4-21-21-2-211-20-20-1-111-1-11100-20201100-2020110020200-1-100-1-100000000000
χ374444-2-2-2-24444444400-2-2-2-2-2-2-2-2000000000000-4-400000000000000000000200000020000000000
χ3844-4-444-4-41-21-2-1-1224-41-21-2-1-122020-2-2-200220000021-100-1-10-2-1100110-202000000000000001-100
χ3944-4-444-4-41-21-2-1-1224-41-21-2-1-1220-202-2-2002200000-211001102-1-100-1-1020-200000000000000-1100
χ4044-4-444-4-41-21-2-1-122-441-21-2-1-122020-22200-2-2000002-1-100-1-10-2110011020-200000000000000-1100
χ4144-4-444-4-41-21-2-1-122-441-21-2-1-1220-2022200-2-200000-2-110011021-100-1-10-202000000000000001-100
χ4244-4-444-4-4-21-2122-1-14-4-21-2122-1-120-2011-1-1-1-1110020-20-1-100-2020110020-200-1-1001100000000000
χ4344-4-444-4-4-21-2122-1-14-4-21-2122-1-1-20201111-1-1-1-100-20-2011002020-1-100-202001100-1-100000000000
χ4444-4-444-4-4-21-2122-1-1-44-21-2122-1-120-20-1-1-1-11111002020-1-100-20-201100-202001100-1-100000000000
χ4544-4-444-4-4-21-2122-1-1-44-21-2122-1-1-2020-1-11111-1-100-2020110020-20-1-10020-200-1-1001100000000000
χ4644-4-4-2-2224444-4-4-4-400-2-2-2-222220000000000004-400000000000000000000-200000020000000000
χ474-44i−4i4-44i−4i44-4-44i−4i4i−4i0044-4-44i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ484-44i−4i4-44i−4i-212-1−2i2ii−i00-212-1−2i2ii−i00003-3−i3i33i−3i3−3000000−i3i30000003−30000000−i3i3003−300000000000
χ494-44i−4i4-44i−4i-212-1−2i2ii−i00-212-1−2i2ii−i00003-3i3−i33i−3i−33000000i3−i3000000−330000000i3−i300−3300000000000
χ504-44i−4i4-44i−4i-212-1−2i2ii−i00-212-1−2i2ii−i0000-33−i3i3−3i3i3−3000000−i3i30000003−30000000i3−i300−3300000000000
χ514-44i−4i4-44i−4i-212-1−2i2ii−i00-212-1−2i2ii−i0000-33i3−i3−3i3i−33000000i3−i3000000−330000000−i3i3003−300000000000
χ524-44i−4i-22−2i2i44-4-44i−4i4i−4i00-2-222−2i2i−2i2i000000000000000000000000000000000000000000i6−i66−6000000
χ534-44i−4i-22−2i2i44-4-44i−4i4i−4i00-2-222−2i2i−2i2i000000000000000000000000000000000000000000−i6i6−66000000
χ544-4−4i4i4-4−4i4i44-4-4−4i4i−4i4i0044-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ554-4−4i4i4-4−4i4i-212-12i−2i−ii00-212-12i−2i−ii00003-3−i3i3−3i3i−33000000−i3i3000000−330000000−i3i300−3300000000000
χ564-4−4i4i4-4−4i4i-212-12i−2i−ii00-212-12i−2i−ii00003-3i3−i3−3i3i3−3000000i3−i30000003−30000000i3−i3003−300000000000
χ574-4−4i4i4-4−4i4i-212-12i−2i−ii00-212-12i−2i−ii0000-33−i3i33i−3i−33000000−i3i3000000−330000000i3−i3003−300000000000
χ584-4−4i4i4-4−4i4i-212-12i−2i−ii00-212-12i−2i−ii0000-33i3−i33i−3i3−3000000i3−i30000003−30000000−i3i300−3300000000000
χ594-4−4i4i-222i−2i44-4-4−4i4i−4i4i00-2-2222i−2i2i−2i000000000000000000000000000000000000000000i6−i6−66000000
χ604-4−4i4i-222i−2i44-4-4−4i4i−4i4i00-2-2222i−2i2i−2i000000000000000000000000000000000000000000−i6i66−6000000
χ618888-4-4-4-42-42-422-4-400-12-12-1-122040400000000000-20-200110-20-200110000000000000000000000
χ628888-4-4-4-42-42-422-4-400-12-12-1-1220-40-40000000000020200-1-1020200-1-10000000000000000000000
χ638888-4-4-4-4-42-42-4-422002-12-122-1-1404000-2-200-2-200-20001100-200011000000000000000000000000
χ648888-4-4-4-4-42-42-4-422002-12-122-1-1-40-4000220022002000-1-1002000-1-1000000000000000000000000
χ6588-8-8-4-4442-42-4-2-24400-12-1211-2-2040-400000000000-20-20011020200-1-10000000000000000000000
χ6688-8-8-4-4442-42-4-2-24400-12-1211-2-20-4040000000000020200-1-10-20-200110000000000000000000000
χ6788-8-8-4-444-42-4244-2-2002-12-1-2-21140-4000-2-2002200-200011002000-1-1000000000000000000000000
χ6888-8-8-4-444-42-4244-2-2002-12-1-2-211-4040002200-2-2002000-1-100-200011000000000000000000000000
χ698-88i−8i8-88i−8i2-4-242i−2i−4i4i002-4-242i−2i−4i4i0000000000000000000000000000000000000000000000000000
χ708-88i−8i-44−4i4i2-4-242i−2i−4i4i00-121-2−ii2i−2i000000000000000000003-30000003i−3i0000000000000000000000
χ718-88i−8i-44−4i4i2-4-242i−2i−4i4i00-121-2−ii2i−2i00000000000000000000-33000000−3i3i0000000000000000000000
χ728-88i−8i-44−4i4i-424-2−4i4i2i−2i002-1-212i−2i−ii000000−2i32i30023−23000000i3−i3000000−33000000000000000000000000
χ738-88i−8i-44−4i4i-424-2−4i4i2i−2i002-1-212i−2i−ii0000002i3−2i300−2323000000−i3i30000003−3000000000000000000000000
χ748-8−8i8i8-8−8i8i2-4-24−2i2i4i−4i002-4-24−2i2i4i−4i0000000000000000000000000000000000000000000000000000
χ758-8−8i8i-444i−4i2-4-24−2i2i4i−4i00-121-2i−i−2i2i000000000000000000003-3000000−3i3i0000000000000000000000
χ768-8−8i8i-444i−4i2-4-24−2i2i4i−4i00-121-2i−i−2i2i00000000000000000000-330000003i−3i0000000000000000000000
χ778-8−8i8i-444i−4i-424-24i−4i−2i2i002-1-21−2i2ii−i000000−2i32i300−2323000000i3−i30000003−3000000000000000000000000
χ788-8−8i8i-444i−4i-424-24i−4i−2i2i002-1-21−2i2ii−i0000002i3−2i30023−23000000−i3i3000000−33000000000000000000000000

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