Finite Group Databasebeta

← Group #13107638

Character table — Group #13107638

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size112222244444455558888888810101010101010101010202020202020202020202020202025255050505050112222244444455558888888810101010101010101010202020202020202020202020202025255050505050
order12255101051010101010224455101010101010244444101010101010202020202020202020202020444444422210101010101010101010224410101010101010102444441010101010102020202020202020202020204444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ3111111111111111-1-1111111111-11111111111-1-1-1-111111111-1-1-1-1-1-1-1111111111111111-1-1111111111-11111111111-1-1-1-111111111-1-1-1-1-1-1-1
χ4111111111111111-1-1111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-11111111111-11ii−i−i-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1ii−i−i1111111111111-1-11111111111-11ii−i−i-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1ii−i−i
χ61111111111111-1-11111111111-11−i−iii-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1−i−iii1111111111111-1-11111111111-11−i−iii-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1−i−iii
χ71111111111111-1-1-1-111111111-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111−i−iii1111111111111-1-1-1-111111111-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111−i−iii
χ81111111111111-1-1-1-111111111-1-1−i−iii-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111ii−i−i1111111111111-1-1-1-111111111-1-1−i−iii-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111ii−i−i
χ911-111111-1-1-1-1111111111-1-1-1-1-1-11-11-11111-1-111-1-111-1-111-1-111-11-11-111-111111-1-1-1-1111111111-1-1-1-1-1-11-11-11111-1-111-1-111-1-111-1-111-11-11-1
χ1011-111111-1-1-1-1111111111-1-1-1-1-1-1-11-111111-1-111-1-1-1-111-1-11111-1-11-1111-111111-1-1-1-1111111111-1-1-1-1-1-1-11-111111-1-111-1-1-1-111-1-11111-1-11-11
χ1111-111111-1-1-1-1111-1-11111-1-1-1-1-111-11-11111-1-1-1-11111-1-111-1-1-1-11-11-1111-111111-1-1-1-1111-1-11111-1-1-1-1-111-11-11111-1-1-1-11111-1-111-1-1-1-11-11-11
χ1211-111111-1-1-1-1111-1-11111-1-1-1-1-11-11-111111-1-1-1-111-1-111-1-111-1-111-11-111-111111-1-1-1-1111-1-11111-1-1-1-1-11-11-111111-1-1-1-111-1-111-1-111-1-111-11-1
χ1311-111111-1-1-1-11-1-1111111-1-1-1-11-1i−i−ii-1-1-1-11111-1-1ii−i−i−i−iii-1-11i−i−ii11-111111-1-1-1-11-1-1111111-1-1-1-11-1i−i−ii-1-1-1-11111-1-1ii−i−i−i−iii-1-11i−i−ii
χ1411-111111-1-1-1-11-1-1111111-1-1-1-11-1−iii−i-1-1-1-11111-1-1−i−iiiii−i−i-1-11−iii−i11-111111-1-1-1-11-1-1111111-1-1-1-11-1−iii−i-1-1-1-11111-1-1−i−iiiii−i−i-1-11−iii−i
χ1511-111111-1-1-1-11-1-1-1-11111-1-1-1-111i−i−ii-1-1-1-111-1-111ii−i−i−i−iii11-1−iii−i11-111111-1-1-1-11-1-1-1-11111-1-1-1-111i−i−ii-1-1-1-111-1-111ii−i−i−i−iii11-1−iii−i
χ1611-111111-1-1-1-11-1-1-1-11111-1-1-1-111−iii−i-1-1-1-111-1-111−i−iiiii−i−i11-1i−i−ii11-111111-1-1-1-11-1-1-1-11111-1-1-1-111−iii−i-1-1-1-111-1-111−i−iiiii−i−i11-1i−i−ii
χ17222−1+52−1−52−1+52−1−522−1+52−1−522222200−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52202222−1+52−1+52−1−52−1−52−1+52−1−520000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000222−1+52−1−52−1+52−1−522−1+52−1−522222200−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52202222−1+52−1+52−1−52−1−52−1+52−1−520000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000
χ18222−1+52−1−52−1+52−1−522−1+52−1−522222200−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5220-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−5200001−521+521−521+521−521+521−521+520000000222−1+52−1−52−1+52−1−522−1+52−1−522222200−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5220-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−5200001−521+521−521+521−521+521−521+520000000
χ19222−1+52−1−52−1+52−1−522−1+52−1−52222-2-200−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-202i2i−2i−2i1−521−521+521+521−521+520000−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ70000000222−1+52−1−52−1+52−1−522−1+52−1−52222-2-200−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-202i2i−2i−2i1−521−521+521+521−521+520000−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ70000000
χ20222−1+52−1−52−1+52−1−522−1+52−1−52222-2-200−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-20−2i−2i2i2i1−521−521+521+521−521+520000ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ70000000222−1+52−1−52−1+52−1−522−1+52−1−52222-2-200−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-20−2i−2i2i2i1−521−521+521+521−521+520000ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ70000000
χ21222−1−52−1+52−1−52−1+522−1−52−1+522222200−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52202222−1−52−1−52−1+52−1+52−1−52−1+520000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000222−1−52−1+52−1−52−1+522−1−52−1+522222200−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52202222−1−52−1−52−1+52−1+52−1−52−1+520000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000
χ22222−1−52−1+52−1−52−1+522−1−52−1+522222200−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5220-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+5200001+521−521+521−521+521−521+521−520000000222−1−52−1+52−1−52−1+522−1−52−1+522222200−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5220-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+5200001+521−521+521−521+521−521+521−520000000
χ23222−1−52−1+52−1−52−1+522−1−52−1+52222-2-200−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-202i2i−2i−2i1+521+521−521−521+521−520000−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ190000000222−1−52−1+52−1−52−1+522−1−52−1+52222-2-200−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-202i2i−2i−2i1+521+521−521−521+521−520000−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ190000000
χ24222−1−52−1+52−1−52−1+522−1−52−1+52222-2-200−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-20−2i−2i2i2i1+521+521−521−521+521−520000ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ190000000222−1−52−1+52−1−52−1+522−1−52−1+52222-2-200−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-20−2i−2i2i2i1+521+521−521−521+521−520000ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ190000000
χ2522-2−1+52−1−52−1+52−1−5221−521+52-2-222200−1+52−1−52−1+52−1−521−521−521+521+52-202-22-2−1+52−1+52−1−52−1−521−521+520000−1+52−1−521−521+52−1+52−1−521−521+52000000022-2−1+52−1−52−1+52−1−5221−521+52-2-222200−1+52−1−52−1+52−1−521−521−521+521+52-202-22-2−1+52−1+52−1−52−1−521−521+520000−1+52−1−521−521+52−1+52−1−521−521+520000000
χ2622-2−1+52−1−52−1+52−1−5221−521+52-2-222200−1+52−1−52−1+52−1−521−521−521+521+52-20-22-22−1+52−1+52−1−52−1−521−521+5200001−521+52−1+52−1−521−521+52−1+52−1−52000000022-2−1+52−1−52−1+52−1−5221−521+52-2-222200−1+52−1−52−1+52−1−521−521−521+521+52-20-22-22−1+52−1+52−1−52−1−521−521+5200001−521+52−1+52−1−521−521+52−1+52−1−520000000
χ2722-2−1+52−1−52−1+52−1−5221−521+52-2-22-2-200−1+52−1−52−1+52−1−521−521−521+521+52202i−2i−2i2i1−521−521+521+52−1+52−1−520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000022-2−1+52−1−52−1+52−1−5221−521+52-2-22-2-200−1+52−1−52−1+52−1−521−521−521+521+52202i−2i−2i2i1−521−521+521+52−1+52−1−520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000
χ2822-2−1+52−1−52−1+52−1−5221−521+52-2-22-2-200−1+52−1−52−1+52−1−521−521−521+521+5220−2i2i2i−2i1−521−521+521+52−1+52−1−520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000022-2−1+52−1−52−1+52−1−5221−521+52-2-22-2-200−1+52−1−52−1+52−1−521−521−521+521+5220−2i2i2i−2i1−521−521+521+52−1+52−1−520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000
χ2922-2−1−52−1+52−1−52−1+5221+521−52-2-222200−1−52−1+52−1−52−1+521+521+521−521−52-202-22-2−1−52−1−52−1+52−1+521+521−520000−1−52−1+521+521−52−1−52−1+521+521−52000000022-2−1−52−1+52−1−52−1+5221+521−52-2-222200−1−52−1+52−1−52−1+521+521+521−521−52-202-22-2−1−52−1−52−1+52−1+521+521−520000−1−52−1+521+521−52−1−52−1+521+521−520000000
χ3022-2−1−52−1+52−1−52−1+5221+521−52-2-222200−1−52−1+52−1−52−1+521+521+521−521−52-20-22-22−1−52−1−52−1+52−1+521+521−5200001+521−52−1−52−1+521+521−52−1−52−1+52000000022-2−1−52−1+52−1−52−1+5221+521−52-2-222200−1−52−1+52−1−52−1+521+521+521−521−52-20-22-22−1−52−1−52−1+52−1+521+521−5200001+521−52−1−52−1+521+521−52−1−52−1+520000000
χ3122-2−1−52−1+52−1−52−1+5221+521−52-2-22-2-200−1−52−1+52−1−52−1+521+521+521−521−52202i−2i−2i2i1+521+521−521−52−1−52−1+520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000022-2−1−52−1+52−1−52−1+5221+521−52-2-22-2-200−1−52−1+52−1−52−1+521+521+521−521−52202i−2i−2i2i1+521+521−521−52−1−52−1+520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000
χ3222-2−1−52−1+52−1−52−1+5221+521−52-2-22-2-200−1−52−1+52−1−52−1+521+521+521−521−5220−2i2i2i−2i1+521+521−521−52−1−52−1+520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000022-2−1−52−1+52−1−52−1+5221+521−52-2-22-2-200−1−52−1+52−1−52−1+521+521+521−521−5220−2i2i2i−2i1+521+521−521−52−1−52−1+520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000
χ332-2022-2-220000-22-22i−2i22-2-200000000002-22-2002i−2i00000000002i−2i000002-2022-2-220000-22-22i−2i22-2-200000000002-22-2002i−2i00000000002i−2i00000
χ342-2022-2-220000-22-2−2i2i22-2-200000000002-22-200−2i2i0000000000−2i2i000002-2022-2-220000-22-2−2i2i22-2-200000000002-22-200−2i2i0000000000−2i2i00000
χ352-2022-2-220000-2-222i−2i22-2-20000000000-22-22002i−2i0000000000−2i2i000002-2022-2-220000-2-222i−2i22-2-20000000000-22-22002i−2i0000000000−2i2i00000
χ362-2022-2-220000-2-22−2i2i22-2-20000000000-22-2200−2i2i00000000002i−2i000002-2022-2-220000-2-22−2i2i22-2-20000000000-22-2200−2i2i00000000002i−2i00000
χ374444444-144-1-1-10044-1-1-1-1-1-1-1-1040000000000-1-1-1-10000000000000004444444-144-1-1-10044-1-1-1-1-1-1-1-1040000000000-1-1-1-1000000000000000
χ384444444-144-1-1-100-4-4-1-1-1-1-1-1-1-10-4000000000011110000000000000004444444-144-1-1-100-4-4-1-1-1-1-1-1-1-10-400000000001111000000000000000
χ3944-44444-1-4-411-10044-1-1-1-111110-40000000000-1-11100000000000000044-44444-1-4-411-10044-1-1-1-111110-40000000000-1-111000000000000000
χ4044-44444-1-4-411-100-4-4-1-1-1-1111104000000000011-1-100000000000000044-44444-1-4-411-100-4-4-1-1-1-1111104000000000011-1-1000000000000000
χ414-4044-4-4-1005−51004i−4i-1-1115−55−5000000000000−iii5−i50000000000000004-4044-4-4-1005−51004i−4i-1-1115−55−5000000000000−iii5−i5000000000000000
χ424-4044-4-4-1005−5100−4i4i-1-1115−55−5000000000000i−i−i5i50000000000000004-4044-4-4-1005−5100−4i4i-1-1115−55−5000000000000i−i−i5i5000000000000000
χ434-4044-4-4-100−551004i−4i-1-111−55−55000000000000−ii−i5i50000000000000004-4044-4-4-100−551004i−4i-1-111−55−55000000000000−ii−i5i5000000000000000
χ444-4044-4-4-100−55100−4i4i-1-111−55−55000000000000i−ii5−i50000000000000004-4044-4-4-100−55100−4i4i-1-111−55−55000000000000i−ii5−i5000000000000000
χ454-40−1+5−1−51−51+540000-44-400−1+5−1−51−51+50000000000−1+51−5−1−51+50000000000000000000004-40−1+5−1−51−51+540000-44-400−1+5−1−51−51+50000000000−1+51−5−1−51+5000000000000000000000
χ464-40−1+5−1−51−51+540000-4-4400−1+5−1−51−51+500000000001−5−1+51+5−1−50000000000000000000004-40−1+5−1−51−51+540000-4-4400−1+5−1−51−51+500000000001−5−1+51+5−1−5000000000000000000000
χ474-40−1−5−1+51+51−540000-44-400−1−5−1+51+51−50000000000−1−51+5−1+51−50000000000000000000004-40−1−5−1+51+51−540000-44-400−1−5−1+51+51−50000000000−1−51+5−1+51−5000000000000000000000
χ484-40−1−5−1+51+51−540000-4-4400−1−5−1+51+51−500000000001+5−1−51−5−1+50000000000000000000004-40−1−5−1+51+51−540000-4-4400−1−5−1+51+51−500000000001+5−1−51−5−1+5000000000000000000000
χ49888−2+25−2−25−2+25−2−25-2−2+25−2−25-2-2-200001−521+521−521+521−521−521+521+520000000000000000000000000000000888−2+25−2−25−2+25−2−25-2−2+25−2−25-2-2-200001−521+521−521+521−521−521+521+520000000000000000000000000000000
χ50888−2−25−2+25−2−25−2+25-2−2−25−2+25-2-2-200001+521−521+521−521+521+521−521−520000000000000000000000000000000888−2−25−2+25−2−25−2+25-2−2−25−2+25-2-2-200001+521−521+521−521+521+521−521−520000000000000000000000000000000
χ5188-8−2+25−2−25−2+25−2−25-22−252+2522-200001−521+521−521+52−1+52−1+52−1−52−1−52000000000000000000000000000000088-8−2+25−2−25−2+25−2−25-22−252+2522-200001−521+521−521+52−1+52−1+52−1−52−1−520000000000000000000000000000000
χ5288-8−2−25−2+25−2−25−2+25-22+252−2522-200001+521−521+521−52−1−52−1−52−1+52−1+52000000000000000000000000000000088-8−2−25−2+25−2−25−2+25-22+252−2522-200001+521−521+521−52−1−52−1−52−1+52−1+520000000000000000000000000000000
χ538-80−2+25−2−252−252+25-20025−25200001−521+52−1+52−1−525−52−5+52−5−525+5200000000000000000000000000000008-80−2+25−2−252−252+25-20025−25200001−521+52−1+52−1−525−52−5+52−5−525+520000000000000000000000000000000
χ548-80−2+25−2−252−252+25-200−2525200001−521+52−1+52−1−52−5+525−525+52−5−5200000000000000000000000000000008-80−2+25−2−252−252+25-200−2525200001−521+52−1+52−1−52−5+525−525+52−5−520000000000000000000000000000000
χ558-80−2−25−2+252+252−25-20025−25200001+521−52−1−52−1+52−5−525+525−52−5+5200000000000000000000000000000008-80−2−25−2+252+252−25-20025−25200001+521−52−1−52−1+52−5−525+525−52−5+520000000000000000000000000000000
χ568-80−2−25−2+252+252−25-200−2525200001+521−52−1−52−1+525+52−5−52−5+525−5200000000000000000000000000000008-80−2−25−2+252+252−25-200−2525200001+521−52−1−52−1+525+52−5−52−5+525−520000000000000000000000000000000
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χ1118-80−2−25−2+252+252−25-20025−25200001+521−52−1−52−1+52−5−525+525−52−5+520000000000000000000000000000000-8802+252−25−2−25−2+25200−2525-20000−1−52−1+521+521−525+52−5−52−5+525−520000000000000000000000000000000
χ1128-80−2−25−2+252+252−25-200−2525200001+521−52−1−52−1+525+52−5−52−5+525−520000000000000000000000000000000-8802+252−25−2−25−2+2520025−25-20000−1−52−1+521+521−52−5−525+525−52−5+520000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.