Finite Group Databasebeta

← Group #13137995

Character table — Group #13137995

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order122234466612123366666641212366612121212441212121212121212121222444888812121212242424242424242446612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111
χ31111111111111111111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-111-1-1
χ511111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111-1-1-11111111111-1-1-1-111-1-1-1-1-1-11-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-11111
χ92222222222222-122-1-12-1222-1-1-1-12-1-1222-1-122-1-1-1-1-1-1002000000-1-1-1-10000000020000-1-1
χ102222222222222-122-1-12-1222-1-1-1-12-1-12-2-2-1-122-1-1-1-1-1-100-2000000111100000000-2000011
χ112222222222222-122-1-12-1-2-2-2-1-1-1-12-1-122211-2-2-1-11111002000000-1-1-1-100000000-2000011
χ122222222222222-122-1-12-1-2-2-2-1-1-1-12-1-12-2-211-2-2-1-1111100-200000011110000000020000-1-1
χ13222222222222-12-1-122-12222-1-1-1-1-122-10022-1-1-1-1-1-1-1-100022002200000000-1-1-1-1000-1-100
χ14222222222222-12-1-122-12222-1-1-1-1-122-10022-1-1-1-1-1-1-1-1000-2-200-2-20000000011110001100
χ15222222222222-12-1-122-12-2-2-2-1-1-1-1-122-100-2-211-1-111110002200-2-2000000001111000-1-100
χ16222222222222-12-1-122-12-2-2-2-1-1-1-1-122-100-2-211-1-11111000-2-2002200000000-1-1-1-10001100
χ1722222-2-2222-2-2222222220002222-2-2-2-2220000-2-2000000-200000022-2-2000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-20000-2-20000002000000-2-222000000000000000
χ1922222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-222−i3i30011−i3−i3i3i300-2000000-1-1110000000000000−i3i3
χ2022222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-222i3−i30011i3i3−i3−i300-2000000-1-1110000000000000i3−i3
χ2122222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-2-2-2−i3i30011−i3−i3i3i300200000011-1-10000000000000i3−i3
χ2222222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-2-2-2i3−i30011i3i3−i3−i300200000011-1-10000000000000−i3i3
χ2322-2-222-2-22-22-222-222-2-2-20002-22-222-2-20000002-200002-2000000000000000000002-20000
χ2422-2-222-2-22-22-222-222-2-2-20002-22-222-2-20000002-20000-2200000000000000000000-220000
χ2522-2-22-22-22-2-2222-222-2-2-20002-22-2-2-222000000-2200000002i−2i00000000000000000002i−2i00
χ2622-2-22-22-22-2-2222-222-2-2-20002-22-2-2-222000000-220000000−2i2i0000000000000000000−2i2i00
χ2722-2-22-22-22-2-22-121-12-21-2000-11-111-22-100003−31-13−33−30002i−2i000000000000−i3−i3i3i3000−ii00
χ2822-2-22-22-22-2-22-121-12-21-2000-11-111-22-100003−31-13−33−3000−2i2i000000000000i3i3−i3−i3000i−i00
χ2922-2-22-22-22-2-22-121-12-21-2000-11-111-22-10000−331-1−33−330002i−2i000000000000i3i3−i3−i3000−ii00
χ3022-2-22-22-22-2-22-121-12-21-2000-11-111-22-10000−331-1−33−33000−2i2i000000000000−i3−i3i3i3000i−i00
χ312-22-22002-2-200222-2-2-2-2200022-2-200002i−2i000000000000000−i2i22−22i−2i00−i2−i2i2i22−22−20000000
χ322-22-22002-2-200222-2-2-2-2200022-2-200002i−2i000000000000000i2−i2−222i−2i00i2i2−i2−i2−22−220000000
χ332-22-22002-2-200222-2-2-2-2200022-2-20000−2i2i000000000000000−i2i2−22−2i2i00−i2−i2i2i2−22−220000000
χ342-22-22002-2-200222-2-2-2-2200022-2-20000−2i2i000000000000000i2−i22−2−2i2i00i2i2−i2−i22−22−20000000
χ35444444444444-2-2-2-2-2-2-2-24441111-2-2-2-200-2-2-2-21111110000000000000000000000000000
χ36444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-200222211-1-1-1-10000000000000000000000000000
χ3744444-4-4444-4-4-24-2-244-24000-2-2-2-22-4-420000002200000000000000000000000000000000
χ3844444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200−2i32i300-1-1i3i3−i3−i30000000000000000000000000000
χ3944444-4-4444-4-4-2-2-2-2-2-2-2-200011112222002i3−2i300-1-1−i3−i3i3i30000000000000000000000000000
χ4044-4-444-4-44-44-44-2-44-22-42000-22-224-22-4000000-2200000000000000000000000000000000
χ4144-4-444-4-44-44-4-242-24-42-4000-22-22-24-42000000-2200000000000000000000000000000000
χ4244-4-444-4-44-44-4-2-22-2-22220001-11-1-2-2220000001-13i−3i−3i3i0000000000000000000000000000
χ4344-4-444-4-44-44-4-2-22-2-22220001-11-1-2-2220000001-1−3i3i3i−3i0000000000000000000000000000
χ4444-4-44-44-44-4-444-2-44-22-42000-22-22-42-240000002-200000000000000000000000000000000
χ4544-4-44-44-44-4-44-2-22-2-22220001-11-122-2-2000023−23-11−33−330000000000000000000000000000
χ4644-4-44-44-44-4-44-2-22-2-22220001-11-122-2-20000−2323-113−33−30000000000000000000000000000
χ474-44-44004-4-4004-24-422-4-2000-2-22200004i−4i0000000000000000000−2i2i00000000000000000
χ484-44-44004-4-4004-24-422-4-2000-2-2220000−4i4i00000000000000000002i−2i00000000000000000
χ494-44-44004-4-400-24-22-4-424000-2-2220000000000000000000000022−2200000000−22−220000000
χ504-44-44004-4-400-24-22-4-424000-2-22200000000000000000000000−2222000000002−22−20000000
χ514-4-44400-4-440044-4-4-444-40004-4-4400000000000000000000000000000000000000000000
χ524-4-44400-4-44004-2-4-42-242000-222-200000000000000000000000000023−23000000000000000
χ534-4-44400-4-44004-2-4-42-242000-222-2000000000000000000000000000−2323000000000000000
χ544-4-44400-4-4400-2422-44-2-4000-222-2000000000000000000000000000000000i6−i6−i6i60000000
χ554-4-44400-4-4400-2422-44-2-4000-222-2000000000000000000000000000000000−i6i6i6−i60000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000002200022000000-1-1-1-100000-1-10000
χ576666-366-3-3-3-3-3000000006-3-300000000000000000000-2-2000-2-2000000111100000110000
χ586666-366-3-3-3-3-300000000-6330000000000000000000022000-2-2000000111100000-1-10000
χ596666-366-3-3-3-3-300000000-63300000000000000000000-2-200022000000-1-1-1-100000110000
χ6066-6-6-36-63-33-3300000000033−33000000000000000000002-2000000000003−33−300000-110000
χ6166-6-6-36-63-33-3300000000033−3300000000000000000000-2200000000000−33−33000001-10000
χ6266-6-6-36-63-33-33000000000−3333000000000000000000002-200000000000−33−3300000-110000
χ6366-6-6-36-63-33-33000000000−333300000000000000000000-22000000000003−33−3000001-10000
χ648-88-88008-8-800-4-4-44444-400022-2-200000000000000000000000000000000000000000000
χ658-8-88800-8-8800-4-4444-4-440002-2-2200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-6-12126-666-600000000000000000000000000000000000000000000000000000000000
χ6812-1212-12-600-66600000000000000000000000000000000000000−2i22i2000000i2i2−i2−i200000000000
χ6912-1212-12-600-666000000000000000000000000000000000000002i2−2i2000000−i2−i2i2i200000000000
χ7012-12-1212-60066-60000000000000000000000000000000000000000000000i6−i6−i6i600000000000
χ7112-12-1212-60066-60000000000000000000000000000000000000000000000−i6i6i6−i600000000000

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