Finite Group Databasebeta

← Group #13166380

Character table — Group #13166380

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222244444444448888888888888888888899991212181818181818242424242424242436363636363636363636363636365454545454545454108108
order12442346121233666121212121233666666661212121212121212121222442424661212666612121212688881224242424242424244444444424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1ii−i−i-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1−i−iii-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911-1-1-1111-1-111-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11-1-1111-1-11111-1-1-1-1-1i−ii−i1ii−i−iii−i−iii−i−iii−i−i1-1
χ1011-1-1-1111-1-111-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11-1-1111-1-11111-1-1-1-1-1−ii−ii1−i−iii−i−iii−i−iii−i−iii1-1
χ1111-1-1-1111-1-111-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1111-1-1-1-1-1-11111-1i−ii−i1ii−i−iii−i−i−i−iii−i−iii-11
χ1211-1-1-1111-1-111-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1111-1-1-1-1-1-11111-1−ii−ii1−i−iii−i−iiiii−i−iii−i−i-11
χ1311-1-1-1111-1-111-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1-1-1111111-1-1-1-111-1-11-111-1-1-1-11111-1-1-1-111-11
χ1411-1-1-1111-1-111-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1-1-1111111-1-1-1-11-111-1-1-1-11111-1-1-1-11111-1-1-11
χ1511-1-1-1111-1-111-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-1-111-1-1-1-1111111-1-11-111-1-1-1-111-1-11111-1-11-1
χ1611-1-1-1111-1-111-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-1-111-1-1-1-111111-111-1-1-1-11111-1-111-1-1-1-1111-1
χ1722222-12-1-1-122-122-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122220022-1-1-1-100000000-12222-1-1-1-1-1-1-1-1-10000000000
χ1822222-12-1-1-122-122-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122220022-1-1-1-100000000-1-2-2-2-2-1111111110000000000
χ1922222-12-1-1-122-122-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200-2-211110000000012i2i−2i−2i1−i−i−i−iiiii0000000000
χ2022222-12-1-1-122-122-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200-2-21111000000001−2i−2i2i2i1iiii−i−i−i−i0000000000
χ212222-22-222222-222-2222222-2-2-2-2-2-222-2-2-2-2-2-22222222200-2-2222200000000-20000-2000000000000000000
χ222222-22-222222-222-2222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-20022-2-2-2-200000000200002000000000000000000
χ232222-2-1-2-1-1-12212212222-1-1-2-21111-1-1-2-21111-1-1-1-1222200-2-2-1-1-1-100000000100001−i3i3−i3i3−i3i3−i3i30000000000
χ242222-2-1-2-1-1-12212212222-1-1-2-21111-1-1-2-21111-1-1-1-1222200-2-2-1-1-1-100000000100001i3−i3i3−i3i3−i3i3−i30000000000
χ252222-2-1-2-1-1-12212212222-1-1-2-21111-1-1-2-21111-1-1-1-1-2-2-2-20022111100000000-10000-13−33−3−33−330000000000
χ262222-2-1-2-1-1-12212212222-1-1-2-21111-1-1-2-21111-1-1-1-1-2-2-2-20022111100000000-10000-1−33−333−33−30000000000
χ2722-2-222-22-2-222222-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222-2-2002-222-2-20000000020000-2000000000000000000
χ2822-2-222-22-2-222222-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22200-22-2-22200000000-200002000000000000000000
χ2922-2-22-1-2-11122-1221-2-2-2-2-1-122-1-1-1-1-1-1-2-21111111122-2-2002-2-1-11100000000-1000013−3−333−3−330000000000
χ3022-2-22-1-2-11122-1221-2-2-2-2-1-122-1-1-1-1-1-1-2-21111111122-2-2002-2-1-11100000000-100001−333−3−333−30000000000
χ3122-2-22-1-2-11122-1221-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111-2-22200-2211-1-10000000010000-1−i3i3i3−i3i3−i3−i3i30000000000
χ3222-2-22-1-2-11122-1221-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111-2-22200-2211-1-10000000010000-1i3−i3−i3i3−i3i3i3−i30000000000
χ3322-2-2-2-12-11122122-1-2-2-2-2-1-1-2-21111-1-122-1-1-1-1111122-2-200-22-1-1110000000012i−2i2i−2i-1−i−iii−i−iii0000000000
χ3422-2-2-2-12-11122122-1-2-2-2-2-1-1-2-21111-1-122-1-1-1-1111122-2-200-22-1-111000000001−2i2i−2i2i-1ii−i−iii−i−i0000000000
χ3522-2-2-2-12-11122122-1-2-2-2-2-1-1-2-21111-1-122-1-1-1-11111-2-222002-211-1-100000000-12-2-221-1-11111-1-10000000000
χ3622-2-2-2-12-11122122-1-2-2-2-2-1-1-2-21111-1-122-1-1-1-11111-2-222002-211-1-100000000-1-222-2111-1-1-1-1110000000000
χ372-22i−2i020-22i−2i220-2-202i2i−2i−2i22000000-2-20000002i2i−2i−2i2-22i−2i00002-22i−2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00
χ382-22i−2i020-22i−2i220-2-202i2i−2i−2i22000000-2-20000002i2i−2i−2i2-22i−2i00002-22i−2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00
χ392-22i−2i020-22i−2i220-2-202i2i−2i−2i22000000-2-20000002i2i−2i−2i-22−2i2i0000-22−2i2i00000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i00
χ402-22i−2i020-22i−2i220-2-202i2i−2i−2i22000000-2-20000002i2i−2i−2i-22−2i2i0000-22−2i2i0000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i00
χ412-2−2i2i020-2−2i2i220-2-20−2i−2i2i2i22000000-2-2000000−2i−2i2i2i2-2−2i2i00002-2−2i2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00
χ422-2−2i2i020-2−2i2i220-2-20−2i−2i2i2i22000000-2-2000000−2i−2i2i2i2-2−2i2i00002-2−2i2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00
χ432-2−2i2i020-2−2i2i220-2-20−2i−2i2i2i22000000-2-2000000−2i−2i2i2i-222i−2i0000-222i−2i00000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00
χ442-2−2i2i020-2−2i2i220-2-20−2i−2i2i2i22000000-2-2000000−2i−2i2i2i-222i−2i0000-222i−2i0000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00
χ4544444444441-241-241-21-21-21-211-2-21-21-211-2-21-21-200004400000011-2-211-2-2000000000000000000000000
χ4644444444441-241-241-21-21-21-211-2-21-21-211-2-21-21-20000-4-4000000-1-122-1-122000000000000000000000000
χ474444444444-214-214-21-21-21-21-2-211-21-21-2-211-21-21000044000000-2-211-2-211000000000000000000000000
χ484444444444-214-214-21-21-21-21-2-211-21-21-2-211-21-210000-4-400000022-1-122-1-1000000000000000000000000
χ494444-44-44441-2-41-2-41-21-21-2-12-1-1221-2-12-1-1221-21-20000000000003-3003-300000000000000000000000000
χ504444-44-44441-2-41-2-41-21-21-2-12-1-1221-2-12-1-1221-21-2000000000000-3300-3300000000000000000000000000
χ514444-44-4444-21-4-21-4-21-21-212-122-1-1-212-122-1-1-21-21000000000000003-3003-3000000000000000000000000
χ524444-44-4444-21-4-21-4-21-21-212-122-1-1-212-122-1-1-21-2100000000000000-3300-33000000000000000000000000
χ5344-4-444-44-4-41-241-2-4-12-121-21-211-2-21-2-12-1-122-12-120000000000003-300-3300000000000000000000000000
χ5444-4-444-44-4-41-241-2-4-12-121-21-211-2-21-2-12-1-122-12-12000000000000-33003-300000000000000000000000000
χ5544-4-444-44-4-4-214-21-42-12-1-21-21-2-211-212-122-1-12-12-1000000000000003-300-33000000000000000000000000
χ5644-4-444-44-4-4-214-21-42-12-1-21-21-2-211-212-122-1-12-12-100000000000000-33003-3000000000000000000000000
χ5744-4-4-4444-4-41-2-41-24-12-121-2-12-1-1221-21-211-2-2-12-1200004-400000011-2-2-1-122000000000000000000000000
χ5844-4-4-4444-4-41-2-41-24-12-121-2-12-1-1221-21-211-2-2-12-120000-44000000-1-12211-2-2000000000000000000000000
χ5944-4-4-4444-4-4-21-4-2142-12-1-212-122-1-1-21-21-2-2112-12-100004-4000000-2-21122-1-1000000000000000000000000
χ6044-4-4-4444-4-4-21-4-2142-12-1-212-122-1-1-21-21-2-2112-12-10000-4400000022-1-1-2-211000000000000000000000000
χ614-44i−4i0-202−2i2i440-4-404i4i−4i−4i-2-200000022000000−2i−2i2i2i4-44i−4i0000-22−2i2i00000000000000000000000000000000
χ624-44i−4i0-202−2i2i440-4-404i4i−4i−4i-2-200000022000000−2i−2i2i2i-44−4i4i00002-22i−2i00000000000000000000000000000000
χ634-4−4i4i0-2022i−2i440-4-40−4i−4i4i4i-2-2000000220000002i2i−2i−2i4-4−4i4i0000-222i−2i00000000000000000000000000000000
χ644-4−4i4i0-2022i−2i440-4-40−4i−4i4i4i-2-2000000220000002i2i−2i−2i-444i−4i00002-2−2i2i00000000000000000000000000000000
χ6588888-48-4-4-42-4-42-4-42-42-4-122-4-1-122-122-4-1-122-12-1200000000000000000000000000000000000000000000
χ6688888-48-4-4-4-42-4-42-4-42-422-1-4222-1-12-1-4222-1-12-12-100000000000000000000000000000000000000000000
χ678888-8-4-8-4-4-42-442-442-42-4-12-2411-2-2-12-2411-2-2-12-1200000000000000000000000000000000000000000000
χ688888-8-4-8-4-4-4-424-424-42-422-14-2-2-2112-14-2-2-2112-12-100000000000000000000000000000000000000000000
χ6988-8-88-4-8-4442-4-42-44-24-24-122-4-1-122-12-2411-2-21-21-200000000000000000000000000000000000000000000
χ7088-8-88-4-8-444-42-4-4244-24-22-1-4222-1-12-14-2-2-211-21-2100000000000000000000000000000000000000000000
χ7188-8-8-8-48-4442-442-4-4-24-24-12-2411-2-2-122-4-1-1221-21-200000000000000000000000000000000000000000000
χ7288-8-8-8-48-444-424-42-44-24-22-14-2-2-2112-1-4222-1-1-21-2100000000000000000000000000000000000000000000
χ738-88i−8i080-88i−8i2-40-2402i−4i−2i4i2-4000000-240000002i−4i−2i4i00000000000000000000000000000000000000000000
χ748-88i−8i080-88i−8i-4204-20−4i2i4i−2i-420000004-2000000−4i2i4i−2i00000000000000000000000000000000000000000000
χ758-88i−8i0-404−4i4i2-40-2402i−4i−2i4i-1200−3i33i3001-20033−3300−i2ii−2i00000000000000000000000000000000000000000000
χ768-88i−8i0-404−4i4i2-40-2402i−4i−2i4i-12003i3−3i3001-200−333300−i2ii−2i00000000000000000000000000000000000000000000
χ778-88i−8i0-404−4i4i-4204-20−4i2i4i−2i2-10000−3i33i3-21000033−332i−i−2ii00000000000000000000000000000000000000000000
χ788-88i−8i0-404−4i4i-4204-20−4i2i4i−2i2-100003i3−3i3-210000−33332i−i−2ii00000000000000000000000000000000000000000000
χ798-8−8i8i080-8−8i8i2-40-240−2i4i2i−4i2-4000000-24000000−2i4i2i−4i00000000000000000000000000000000000000000000
χ808-8−8i8i080-8−8i8i-4204-204i−2i−4i2i-420000004-20000004i−2i−4i2i00000000000000000000000000000000000000000000
χ818-8−8i8i0-4044i−4i2-40-240−2i4i2i−4i-1200−3i33i3001-200−333300i−2i−i2i00000000000000000000000000000000000000000000
χ828-8−8i8i0-4044i−4i2-40-240−2i4i2i−4i-12003i3−3i3001-20033−3300i−2i−i2i00000000000000000000000000000000000000000000
χ838-8−8i8i0-4044i−4i-4204-204i−2i−4i2i2-10000−3i33i3-210000−3333−2ii2i−i00000000000000000000000000000000000000000000
χ848-8−8i8i0-4044i−4i-4204-204i−2i−4i2i2-100003i3−3i3-21000033−33−2ii2i−i00000000000000000000000000000000000000000000

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