Finite Group Databasebeta

← Group #13099903

Character table — Group #13099903

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11112244444444888888888888888888882020202025252525404040404040404050505050505050505050100100100100
order122244551010101010105510101010101020202020202020202020202044444444202020202020202022444444448888
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ51111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−iii
χ61111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiii−i−i
χ71111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ91-1-111-111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1i−ii−i11-1-1ii−i−iii−i−i-1111-1-111-1-1i−ii−i
χ101-1-111-111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1i−ii−i11-1-1ii−i−iii−i−i-11-1-111-1-111−ii−ii
χ111-1-111-111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1i−i−ii-1-111ii−i−i−i−iii1-1ii−i−i−i−iii-111-1
χ121-1-111-111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1i−i−ii-1-111ii−i−i−i−iii1-1−i−iiiii−i−i1-1-11
χ131-1-111-111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1−iii−i-1-111−i−iiiii−i−i1-1ii−i−i−i−iii1-1-11
χ141-1-111-111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1−iii−i-1-111−i−iiiii−i−i1-1−i−iiiii−i−i-111-1
χ151-1-111-111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1−ii−ii11-1-1−i−iii−i−iii-1111-1-111-1-1−ii−ii
χ161-1-111-111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1−ii−ii11-1-1−i−iii−i−iii-11-1-111-1-111i−ii−i
χ172222-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000222200000000-2-2000000000000
χ182222-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-2-20000000022000000000000
χ1922-2-200222-2-2-22-22222-2-2-2-200000000000000002i−2i2i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ2022-2-200222-2-2-22-22222-2-2-2-200000000000000002i−2i2i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ2122-2-200222-2-2-22-22222-2-2-2-20000000000000000−2i2i−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ2222-2-200222-2-2-22-22222-2-2-2-20000000000000000−2i2i−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ232-22-20022-22-2-2-2222-2-222-2-200000000000000002i−2i−2i2i00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ242-22-20022-22-2-2-2222-2-222-2-200000000000000002i−2i−2i2i0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ252-22-20022-22-2-2-2222-2-222-2-20000000000000000−2i2i2i−2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ262-22-20022-22-2-2-2222-2-222-2-20000000000000000−2i2i2i−2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ272-2-22-2222-2-222-2-222-2-2-2-222-2-222-2-2-2-22222000022-2-2000000002-2000000000000
χ282-2-22-2222-2-222-2-222-2-2-2-222-2-222-2-2-2-222220000-2-22200000000-22000000000000
χ294444444-14-14-1-14-1-1-1-1-1-1-1-14-14-1-1-1-1-1-1-1-1-144000000-1-1-1-1000000000000000000
χ304444444-14-14-1-14-1-1-1-1-1-1-1-14-14-1-1-1-1-1-1-1-1-1-4-40000001111000000000000000000
χ31444444-14-14-144-1-1-1-1-1-1-1-1-1-14-14-1-1-1-1-1-1-1-1004400000000-1-1-1-100000000000000
χ32444444-14-14-144-1-1-1-1-1-1-1-1-1-14-14-1-1-1-1-1-1-1-100-4-400000000111100000000000000
χ334444-4-44-14-14-1-14-1-1-1-1-1-1-1-1-41-4111111111000000005−55−5000000000000000000
χ344444-4-44-14-14-1-14-1-1-1-1-1-1-1-1-41-411111111100000000−55−55000000000000000000
χ354444-4-4-14-14-144-1-1-1-1-1-1-1-1-11-41-4111111110000000000005−55−500000000000000
χ364444-4-4-14-14-144-1-1-1-1-1-1-1-1-11-41-411111111000000000000−55−5500000000000000
χ374-4-444-44-1-414-11-4-1-11111-1-14-1-41-1-1-1-111114i−4i000000−i−iii000000000000000000
χ384-4-444-44-1-414-11-4-1-11111-1-14-1-41-1-1-1-11111−4i4i000000ii−i−i000000000000000000
χ394-4-444-4-141-4-14-41-1-11111-1-1-141-4-1-1-1-11111004i−4i00000000−i−iii00000000000000
χ404-4-444-4-141-4-14-41-1-11111-1-1-141-4-1-1-1-1111100−4i4i00000000ii−i−i00000000000000
χ414-4-44-444-1-414-11-4-1-11111-1-1-414-11111-1-1-1-100000000i5−i5−i5i5000000000000000000
χ424-4-44-444-1-414-11-4-1-11111-1-1-414-11111-1-1-1-100000000−i5i5i5−i5000000000000000000
χ434-4-44-44-141-4-14-41-1-11111-1-11-4-141111-1-1-1-1000000000000i5−i5−i5i500000000000000
χ444-4-44-44-141-4-14-41-1-11111-1-11-4-141111-1-1-1-1000000000000−i5i5i5−i500000000000000
χ45888888-2-2-2-2-2-2-2-23-23-23-23-2-2-2-2-233-2-233-2-2000000000000000000000000000000
χ46888888-2-2-2-2-2-2-2-2-23-23-23-23-2-2-2-2-2-233-2-233000000000000000000000000000000
χ478888-8-8-2-2-2-2-2-2-2-23-23-23-23-22222-3-322-3-322000000000000000000000000000000
χ488888-8-8-2-2-2-2-2-2-2-2-23-23-23-23222222-3-322-3-3000000000000000000000000000000
χ4988-8-8008-282-82-2-8-2-2-2-22222000000000000000000000000000000000000000000
χ5088-8-800-28-2-82-882-2-2-2-22222000000000000000000000000000000000000000000
χ5188-8-800-2-2-2222-223-23-2-32-3200005i−5i005i−5i00000000000000000000000000000000
χ5288-8-800-2-2-2222-223-23-2-32-320000−5i5i00−5i5i00000000000000000000000000000000
χ5388-8-800-2-2-2222-22-23-232-32-30000005i−5i005i−5i000000000000000000000000000000
χ5488-8-800-2-2-2222-22-23-232-32-3000000−5i5i00−5i5i000000000000000000000000000000
χ558-88-8008-2-8-2-8228-2-222-2-222000000000000000000000000000000000000000000
χ568-88-800-28282-8-8-2-2-222-2-222000000000000000000000000000000000000000000
χ578-88-800-2-22-2222-23-2-323-2-3200005i−5i00−5i5i00000000000000000000000000000000
χ588-88-800-2-22-2222-23-2-323-2-320000−5i5i005i−5i00000000000000000000000000000000
χ598-88-800-2-22-2222-2-232-3-232-30000005i−5i00−5i5i000000000000000000000000000000
χ608-88-800-2-22-2222-2-232-3-232-3000000−5i5i005i−5i000000000000000000000000000000
χ618-8-888-8-2-222-2-2223-2-32-323-2-2-22233-2-2-3-322000000000000000000000000000000
χ628-8-888-8-2-222-2-222-232-32-3-23-2-222-2-23322-3-3000000000000000000000000000000
χ638-8-88-88-2-222-2-2223-2-32-323-222-2-2-3-32233-2-2000000000000000000000000000000
χ648-8-88-88-2-222-2-222-232-32-3-2322-2-222-3-3-2-233000000000000000000000000000000

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