Finite Group Databasebeta

← Group #13103389

Character table — Group #13103389

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size1128888888810101010161620202020252525252525404040405050505050505080808080100100100100
order1225551010101010444410102244448888202020204888888101020208888
χ11111111111111111111111111111111111111111111111
χ2111111111111111111-11-111-1-1-1-111111-1-1-1-1-1-11-11-111-1-1
χ311111111111111111-11-1111-1-1-1-111111-1-1-1-1-1-1-11-11-1-111
χ411111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1
χ511111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1
χ611111111111-1-1-1-1111-11-1111111-1-1-1-1111-1-1-1-11-11-1-1-111
χ711111111111-1-1-1-111-11-11111111-1-1-1-1111-1-1-1-1-11-1111-1-1
χ811111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111
χ911-11111-111-1ii−i−i-1-111-1-1-1-1ii−i−iii−i−i1i−i11-1-111-1-1i−ii−i
χ1011-11111-111-1ii−i−i-1-11-1-11-1-1−i−iiiii−i−i1−ii-1-1111-1-11i−i−ii
χ1111-11111-111-1ii−i−i-1-1-111-1-1-1−i−iiiii−i−i1−ii-1-111-111-1−iii−i
χ1211-11111-111-1ii−i−i-1-1-1-111-1-1ii−i−iii−i−i1i−i11-1-1-1-111−ii−ii
χ1311-11111-111-1−i−iii-1-111-1-1-1-1−i−iii−i−iii1−ii11-1-111-1-1−ii−ii
χ1411-11111-111-1−i−iii-1-11-1-11-1-1ii−i−i−i−iii1i−i-1-1111-1-11−iii−i
χ1511-11111-111-1−i−iii-1-1-111-1-1-1ii−i−i−i−iii1i−i-1-111-111-1i−i−ii
χ1611-11111-111-1−i−iii-1-1-1-111-1-1−i−iii−i−iii1−ii11-1-1-1-111i−ii−i
χ17222222222220000220000-2-22i2i−2i−2i0000-2−2i2i000000000000
χ18222222222220000220000-2-2−2i−2i2i2i0000-22i−2i000000000000
χ1922-22222-222-20000-2-200002222220000-2-2-2000000000000
χ2022-22222-222-20000-2-2000022-2-2-2-20000-222000000000000
χ212-20222-20-2-201+i−1−i1−i−1+i0000002i−2i2ζ−2ζ2ζ3−2ζ31+i−1−i1−i−1+i0002−2i2−i200000000
χ222-20222-20-2-201+i−1−i1−i−1+i0000002i−2i−2ζ2ζ−2ζ32ζ31+i−1−i1−i−1+i000−22−i2i200000000
χ232-20222-20-2-201−i−1+i1+i−1−i000000−2i2i2ζ3−2ζ32ζ−2ζ1−i−1+i1+i−1−i000−22i2−i200000000
χ242-20222-20-2-201−i−1+i1+i−1−i000000−2i2i−2ζ32ζ3−2ζ2ζ1−i−1+i1+i−1−i0002−2−i2i200000000
χ252-20222-20-2-20−1+i1−i−1−i1+i000000−2i2i2ζ3−2ζ32ζ−2ζ−1+i1−i−1−i1+i0002−2−i2i200000000
χ262-20222-20-2-20−1+i1−i−1−i1+i000000−2i2i−2ζ32ζ3−2ζ2ζ−1+i1−i−1−i1+i000−22i2−i200000000
χ272-20222-20-2-20−1−i1+i−1+i1−i0000002i−2i2ζ−2ζ2ζ3−2ζ3−1−i1+i−1+i1−i000−22−i2i200000000
χ282-20222-20-2-20−1−i1+i−1+i1−i0000002i−2i−2ζ2ζ−2ζ32ζ3−1−i1+i−1+i1−i0002−2i2−i200000000
χ298883-2-233-2-234444-2-20000000000-1-1-1-1000000000000000
χ308883-2-233-2-23-4-4-4-4-2-200000000001111000000000000000
χ31888-23-2-2-23-2-200003-20404000000000000000000-10-10000
χ32888-23-2-2-23-2-200003-20-40-40000000000000000001010000
χ33888-2-23-2-2-23-20000-23404000000000000000000-10-100000
χ34888-2-23-2-2-23-20000-23-40-400000000000000000010100000
χ3588-83-2-23-3-2-2-34i4i−4i−4i220000000000−i−iii000000000000000
χ3688-83-2-23-3-2-2-3−4i−4i4i4i220000000000ii−i−i000000000000000
χ3788-8-23-2-223-220000-32040-4000000000000000000-1010000
χ3888-8-23-2-223-220000-320-40400000000000000000010-10000
χ3988-8-2-23-22-23200002-340-4000000000000000000-10100000
χ4088-8-2-23-22-23200002-3-40400000000000000000010-100000
χ418-803-2-2-3522-54-44-4000000000000-11-11000000000000000
χ428-803-2-2-3522-5-44-440000000000001-11-1000000000000000
χ438-803-2-2-3-52254i−4i−4i4i000000000000−iii−i000000000000000
χ448-803-2-2-3-5225−4i4i4i−4i000000000000i−i−ii000000000000000
χ4516-160-46-440-64000000000000000000000000000000000000
χ4616-160-4-46404-6000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.