Finite Group Databasebeta

← Group #13167579

Character table — Group #13167579

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222244444444444444888888888888888888181818181818181836363636363636363636363636363636363636363636363636363636363672727272
order12222236663366666666666633666666666666666644441212121244444444888812121212121212121212242424242424242412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-1-1111111-1-1111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-11-1-11111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111-1-1111111-1-1111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ71111-1-1111111-1-1111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ81111-1-1111111-1-1111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ911-1-11-11-1-11111-111-111-1-1-1-1-1111-111-1-1-1-11111-1-1-1-1-11-11-1-111i−ii−ii−ii−i1-11-11-1ii−i−iii−i−i11-1-111-1-1i−ii−i
χ1011-1-11-11-1-11111-111-111-1-1-1-1-1111-111-1-1-1-11111-1-1-1-1-11-11-1-111i−ii−i−ii−ii-11-111-1−i−iii−i−iii-1-111-1-111i−ii−i
χ1111-1-11-11-1-11111-111-111-1-1-1-1-1111-111-1-1-1-11111-1-1-1-1-11-11-1-111−ii−iii−ii−i-11-111-1ii−i−iii−i−i-1-111-1-111−ii−ii
χ1211-1-11-11-1-11111-111-111-1-1-1-1-1111-111-1-1-1-11111-1-1-1-1-11-11-1-111−ii−ii−ii−ii1-11-11-1−i−iii−i−iii11-1-111-1-1−ii−ii
χ1311-1-1-111-1-1111-1111-1-1-111-1-1-111-1111-1-1-1-1-1-1-1-11111-1-111-1-111i−i−iii−i−ii1-1-11-11ii−i−i−i−iii11-1-1-1-111i−i−ii
χ1411-1-1-111-1-1111-1111-1-1-111-1-1-111-1111-1-1-1-1-1-1-1-11111-1-111-1-111i−i−ii−iii−i-111-1-11−i−iiiii−i−i-1-11111-1-1i−i−ii
χ1511-1-1-111-1-1111-1111-1-1-111-1-1-111-1111-1-1-1-1-1-1-1-11111-1-111-1-111−iii−ii−i−ii-111-1-11ii−i−i−i−iii-1-11111-1-1−iii−i
χ1611-1-1-111-1-1111-1111-1-1-111-1-1-111-1111-1-1-1-1-1-1-1-11111-1-111-1-111−iii−i−iii−i1-1-11-11−i−iiiii−i−i11-1-1-1-111−iii−i
χ17222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2000000000000-2-200000000000000000000
χ18222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1000000002222-1-100000000-1-1-1-1-1-1-1-10000
χ19222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100000000-2-2-2-2-1-100000000111111110000
χ20222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100000000000011000000003−33−33−33−30000
χ21222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000000000001100000000−33−33−33−330000
χ222222-2-2222222-2-2222-2-2-2-222222-2-2222222-2-2-2-2-2-2-2-2-222-2-2-2-2-20000000000002200000000000000000000
χ232222-2-2-1-1-1-12211222-2-2-2-2222-1-1-2-2-1-1-1-1-1-1111111112-2-22-1-1-1-10000000022-2-21100000000-1-1-1-111110000
χ242222-2-2-1-1-1-12211222-2-2-2-2222-1-1-2-2-1-1-1-1-1-1111111112-2-22-1-1-1-100000000-2-22211000000001111-1-1-1-10000
χ252222-2-2-1-1-1-12211222-2-2-2-2222-1-1-2-2-1-1-1-1-1-111111111-222-21111000000000000-1-1000000003−33−3−33−330000
χ262222-2-2-1-1-1-12211222-2-2-2-2222-1-1-2-2-1-1-1-1-1-111111111-222-21111000000000000-1-100000000−33−333−33−30000
χ2722-2-22-22-2-22222-222-222-2-2-2-2-2222-222-2-2-2-22222-2-2-2-22-22-222-2-2000000000000-2200000000000000000000
χ2822-2-22-2-111-122-1122-222-2-2-2-2-2-1-12-2-1-11111-1-1-1-111112-22-2-1-1110000000000001-1000000003−3−333−3−330000
χ2922-2-22-2-111-122-1122-222-2-2-2-2-2-1-12-2-1-11111-1-1-1-111112-22-2-1-1110000000000001-100000000−333−3−333−30000
χ3022-2-22-2-111-122-1122-222-2-2-2-2-2-1-12-2-1-11111-1-1-1-11111-22-2211-1-1000000002-22-2-1100000000-1-111-1-1110000
χ3122-2-22-2-111-122-1122-222-2-2-2-2-2-1-12-2-1-11111-1-1-1-11111-22-2211-1-100000000-22-22-110000000011-1-111-1-10000
χ3222-2-2-222-2-2222-2222-2-2-222-2-2-222-2222-2-2-2-2-2-2-2-2222222-2-222-2-20000000000002-200000000000000000000
χ3322-2-2-22-111-1221-122-2-2-222-2-2-2-1-1-22-1-111111111-1-1-1-122-2-2-1-111000000000000-11000000003−3−33−333−30000
χ3422-2-2-22-111-1221-122-2-2-222-2-2-2-1-1-22-1-111111111-1-1-1-122-2-2-1-111000000000000-1100000000−333−33−3−330000
χ3522-2-2-22-111-1221-122-2-2-222-2-2-2-1-1-22-1-111111111-1-1-1-1-2-22211-1-1000000002-2-221-100000000-1-11111-1-10000
χ3622-2-2-22-111-1221-122-2-2-222-2-2-2-1-1-22-1-111111111-1-1-1-1-2-22211-1-100000000-222-21-10000000011-1-1-1-1110000
χ3744444444441-2441-211111-2-211-2-2-21-211-2-211-2-211-2-20000000000002222000000-1-1-1-1-1-1-1-1000000000000
χ3844444444441-2441-211111-2-211-2-2-21-211-2-211-2-211-2-2000000000000-2-2-2-200000011111111000000000000
χ394444444444-2144-21-2-2-2-2-211-2-2111-21-2-211-2-211-2-21100000000222200000000000000000000000000-1-1-1-1
χ404444444444-2144-21-2-2-2-2-211-2-2111-21-2-211-2-211-2-21100000000-2-2-2-2000000000000000000000000001111
χ414444-4-444441-2-4-41-21-1-1-1-1-2-211-2221-211-2-2-1-122-1-12200000000000022-2-2000000-1-1-1-11111000000000000
χ424444-4-444441-2-4-41-21-1-1-1-1-2-211-2221-211-2-2-1-122-1-122000000000000-2-2220000001111-1-1-1-1000000000000
χ434444-4-44444-21-4-4-21-2222211-2-21-1-1-21-2-21122-1-122-1-10000000022-2-200000000000000000000000000-1-111
χ444444-4-44444-21-4-4-21-2222211-2-21-1-1-21-2-21122-1-122-1-100000000-2-2220000000000000000000000000011-1-1
χ4544-4-44-44-4-441-24-41-2-111-1-122-11-2-221-2-1-12211-2-2-1-1220000000000002i−2i2i−2i000000−i−iii−i−iii000000000000
χ4644-4-44-44-4-441-24-41-2-111-1-122-11-2-221-2-1-12211-2-2-1-122000000000000−2i2i−2i2i000000ii−i−iii−i−i000000000000
χ4744-4-44-44-4-44-214-4-212-2-222-1-12-211-1-2122-1-1-2-21122-1-1000000002i−2i2i−2i00000000000000000000000000−ii−ii
χ4844-4-44-44-4-44-214-4-212-2-222-1-12-211-1-2122-1-1-2-21122-1-100000000−2i2i−2i2i00000000000000000000000000i−ii−i
χ4944-4-4-444-4-441-2-441-2-1-1-11122-11-22-21-2-1-122-1-12211-2-20000000000002i−2i−2i2i000000−i−iiiii−i−i000000000000
χ5044-4-4-444-4-441-2-441-2-1-1-11122-11-22-21-2-1-122-1-12211-2-2000000000000−2i2i2i−2i000000ii−i−i−i−iii000000000000
χ5144-4-4-444-4-44-21-44-21222-2-2-1-12-21-11-2122-1-122-1-1-2-211000000002i−2i−2i2i00000000000000000000000000−iii−i
χ5244-4-4-444-4-44-21-44-21222-2-2-1-12-21-11-2122-1-122-1-1-2-21100000000−2i2i2i−2i00000000000000000000000000i−i−ii
χ534-44-40044-4-41-200-1213-33-32-2-11-200-121-12-23-3003-30000000000000000000000003−33−33−33−3000000000000
χ544-44-40044-4-41-200-1213-33-32-2-11-200-121-12-23-3003-3000000000000000000000000−33−33−33−33000000000000
χ554-44-40044-4-41-200-121-33-332-2-11-200-121-12-2-3300-330000000000000000000000003−33−3−33−33000000000000
χ564-44-40044-4-41-200-121-33-332-2-11-200-121-12-2-3300-33000000000000000000000000−33−333−33−3000000000000
χ574-44-40044-4-44400-4-440000-44-44400-4-44-4-4400000000000000000000000000000000000000000000000000
χ584-44-400-2-2224400-4-440000-44-4-2-20022-222-200000000000023−2323−230000000000000000000000000000000000
χ594-44-400-2-2224400-4-440000-44-4-2-20022-222-2000000000000−2323−23230000000000000000000000000000000000
χ604-4-44004-44-41-200-12-13-3-33-2211-200-12-11-223-300-33000000000000000000000000−i3i3i3−i3−i3i3i3−i3000000000000
χ614-4-44004-44-41-200-12-13-3-33-2211-200-12-11-223-300-33000000000000000000000000i3−i3−i3i3i3−i3−i3i3000000000000
χ624-4-44004-44-41-200-12-1-333-3-2211-200-12-11-22-33003-3000000000000000000000000−i3i3i3−i3i3−i3−i3i3000000000000
χ634-4-44004-44-41-200-12-1-333-3-2211-200-12-11-22-33003-3000000000000000000000000i3−i3−i3i3−i3i3i3−i3000000000000
χ644-4-44004-44-44400-4-4-400004-444400-4-4-444-400000000000000000000000000000000000000000000000000
χ654-4-4400-22-224400-4-4-400004-44-2-200222-2-2200000000000023−23−23230000000000000000000000000000000000
χ664-4-4400-22-224400-4-4-400004-44-2-200222-2-22000000000000−232323−230000000000000000000000000000000000
χ67888888-4-4-4-42-4-4-42-422222-4-42-12-4-4-12-1-122-1-122-1-122000000000000000000000000000000000000000000
χ68888888-4-4-4-4-42-4-4-42-4-4-4-4-422-42-1222-122-1-122-1-122-1-1000000000000000000000000000000000000000000
χ698888-8-8-4-4-4-42-4442-42-2-2-2-2-4-42-1244-12-1-12211-2-211-2-2000000000000000000000000000000000000000000
χ708888-8-8-4-4-4-4-4244-42-4444422-42-1-2-22-122-1-1-2-211-2-211000000000000000000000000000000000000000000
χ7188-8-88-8-444-42-4-442-4-222-2-244-2-12-44-1211-2-2-1-12211-2-2000000000000000000000000000000000000000000
χ7288-8-88-8-444-4-42-44-424-4-444-2-242-12-22-1-2-21122-1-1-2-211000000000000000000000000000000000000000000
χ7388-8-8-88-444-42-44-42-4-2-2-22244-2-124-4-1211-2-211-2-2-1-122000000000000000000000000000000000000000000
χ7488-8-8-88-444-4-424-4-42444-4-4-2-242-1-222-1-2-211-2-21122-1-1000000000000000000000000000000000000000000
χ758-88-80088-8-8-42004-2-40000-224-42004-2-44-2200000000000000000000000000000000000000000000000000
χ768-88-800-4-4442-400-2426-66-64-4-2-12001-2-11-22-3300-3300000000000000000000000000000000000000000000
χ778-88-800-4-4442-400-242-66-664-4-2-12001-2-11-223-3003-300000000000000000000000000000000000000000000
χ788-88-800-4-444-42004-2-40000-2242-100-212-21-100−3i33i300−3i33i3000000000000000000000000000000000000000000
χ798-88-800-4-444-42004-2-40000-2242-100-212-21-1003i3−3i3003i3−3i3000000000000000000000000000000000000000000
χ808-8-88008-88-8-42004-2400002-2-4-42004-24-42-200000000000000000000000000000000000000000000000000
χ818-8-8800-44-442-400-24-26-6-66-442-12001-21-12-2-33003-300000000000000000000000000000000000000000000
χ828-8-8800-44-442-400-24-2-666-6-442-12001-21-12-23-300-3300000000000000000000000000000000000000000000
χ838-8-8800-44-44-42004-2400002-2-42-100-21-22-1100−3i33i3003i3−3i3000000000000000000000000000000000000000000
χ848-8-8800-44-44-42004-2400002-2-42-100-21-22-11003i3−3i300−3i33i3000000000000000000000000000000000000000000

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