Finite Group Databasebeta

← Group #13022153

Character table — Group #13022153

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122224444444444445555555588888888888888881010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12222222444444445101010101010102222222244442020202020202020202020204444202020202020202044448888888888888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111−i−i−i−iiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111iiii−i−i−i−i
χ9111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ11111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ12111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii
χ1711-1-11-11-111-1-1i−ii−i11-1-11-11-1111-1-1-11-11-1i−i11-1-1ii−i−iii−i−i1-11-111-1-1ii−i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ1811-1-11-11-111-1-1i−ii−i11-1-11-11-1111-1-1-11-11-1i−i11-1-1ii−i−iii−i−i1-11-111-1-1ii−i−ii−ii−i-1-111−i−iii-1-111−i−iii1-1i−i-11−ii-11−ii
χ1911-1-11-11-111-1-1i−ii−i11-1-11-11-1111-1-1-11-1-11−ii11-1-1ii−i−iii−i−i1-11-1-1-111−i−iiii−ii−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii
χ2011-1-11-11-111-1-1i−ii−i11-1-11-11-1111-1-1-11-1-11−ii11-1-1ii−i−iii−i−i1-11-1-1-111−i−iiii−ii−i-1-111−i−iii-1-111−i−iii-11−ii1-1i−i1-1i−i
χ2111-1-11-11-111-1-1i−ii−i11-1-11-11-1-1-1-1111-111-1i−i11-1-1ii−i−iii−i−i-11-1111-1-1ii−i−i−ii−iiii−i−i-1-111−i−iii11-1-1-11−iii−i-11−ii1-1
χ2211-1-11-11-111-1-1i−ii−i11-1-11-11-1-1-1-1111-111-1i−i11-1-1ii−i−iii−i−i-11-1111-1-1ii−i−i−ii−ii−i−iii11-1-1ii−i−i-1-111-11−ii−ii1-1i−i-11
χ2311-1-11-11-111-1-1i−ii−i11-1-11-11-1-1-1-1111-11-11−ii11-1-1ii−i−iii−i−i-11-11-1-111−i−iii−ii−iiii−i−i-1-111−i−iii11-1-11-1i−i−ii1-1i−i-11
χ2411-1-11-11-111-1-1i−ii−i11-1-11-11-1-1-1-1111-11-11−ii11-1-1ii−i−iii−i−i-11-11-1-111−i−iii−ii−ii−i−iii11-1-1ii−i−i-1-1111-1i−ii−i-11−ii1-1
χ2511-1-11-11-111-1-1−ii−ii11-1-11-11-1111-1-1-11-11-1−ii11-1-1−i−iii−i−iii1-11-111-1-1−i−iii−ii−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ2611-1-11-11-111-1-1−ii−ii11-1-11-11-1111-1-1-11-11-1−ii11-1-1−i−iii−i−iii1-11-111-1-1−i−iii−ii−ii-1-111ii−i−i-1-111ii−i−i1-1−ii-11i−i-11i−i
χ2711-1-11-11-111-1-1−ii−ii11-1-11-11-1111-1-1-11-1-11i−i11-1-1−i−iii−i−iii1-11-1-1-111ii−i−i−ii−ii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i
χ2811-1-11-11-111-1-1−ii−ii11-1-11-11-1111-1-1-11-1-11i−i11-1-1−i−iii−i−iii1-11-1-1-111ii−i−i−ii−ii-1-111ii−i−i-1-111ii−i−i-11i−i1-1−ii1-1−ii
χ2911-1-11-11-111-1-1−ii−ii11-1-11-11-1-1-1-1111-111-1−ii11-1-1−i−iii−i−iii-11-1111-1-1−i−iiii−ii−iii−i−i11-1-1−i−iii-1-111-11i−ii−i1-1−ii-11
χ3011-1-11-11-111-1-1−ii−ii11-1-11-11-1-1-1-1111-111-1−ii11-1-1−i−iii−i−iii-11-1111-1-1−i−iiii−ii−i−i−iii-1-111ii−i−i11-1-1-11i−i−ii-11i−i1-1
χ3111-1-11-11-111-1-1−ii−ii11-1-11-11-1-1-1-1111-11-11i−i11-1-1−i−iii−i−iii-11-11-1-111ii−i−ii−ii−iii−i−i11-1-1−i−iii-1-1111-1−ii−ii-11i−i1-1
χ3211-1-11-11-111-1-1−ii−ii11-1-11-11-1-1-1-1111-11-11i−i11-1-1−i−iii−i−iii-11-11-1-111ii−i−ii−ii−i−i−iii-1-111ii−i−i11-1-11-1−iii−i1-1−ii-11
χ3322222222-2-2-2-222-2-222222222222222220000-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-20000000000000000000000000000
χ3422222222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-20000-2-2-2-22222-2-2-2-2222200000000-2-2220000000000000000000000000000
χ3522222222-2-2-2-2-2-22222222222222222220000-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-2220000000000000000000000000000
χ3622222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-2-2-2222222220000000022-2-20000000000000000000000000000
χ3722-2-22-22-2-2-2222i−2i−2i2i22-2-22-22-2222-2-2-22-20000-2-2222i2i−2i−2i−2i−2i2i2i-22-22000000002i−2i−2i2i0000000000000000000000000000
χ3822-2-22-22-2-2-2222i−2i−2i2i22-2-22-22-2-2-2-2222-220000-2-2222i2i−2i−2i−2i−2i2i2i2-22-200000000−2i2i2i−2i0000000000000000000000000000
χ3922-2-22-22-2-2-222−2i2i2i−2i22-2-22-22-2222-2-2-22-20000-2-222−2i−2i2i2i2i2i−2i−2i-22-2200000000−2i2i2i−2i0000000000000000000000000000
χ4022-2-22-22-2-2-222−2i2i2i−2i22-2-22-22-2-2-2-2222-220000-2-222−2i−2i2i2i2i2i−2i−2i2-22-2000000002i−2i−2i2i0000000000000000000000000000
χ412-2222-2-2-22-22-200002-2222-2-2-222-222-2-2-200002-22-2000000002-2-2200000000000000002-22-200002-22-2000000000000
χ422-2222-2-2-22-22-200002-2222-2-2-222-222-2-2-200002-22-2000000002-2-220000000000000000-22-220000-22-22000000000000
χ432-2222-2-2-22-22-200002-2222-2-2-2-2-22-2-222200002-22-200000000-222-200000000000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ442-2222-2-2-22-22-200002-2222-2-2-2-2-22-2-222200002-22-200000000-222-20000000000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ452-2222-2-2-2-22-2200002-2222-2-2-222-222-2-2-20000-22-2200000000-222-20000000000002-22-200002-22-20000000000000000
χ462-2222-2-2-2-22-2200002-2222-2-2-222-222-2-2-20000-22-2200000000-222-2000000000000-22-220000-22-220000000000000000
χ472-2222-2-2-2-22-2200002-2222-2-2-2-2-22-2-22220000-22-22000000002-2-220000000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ482-2222-2-2-2-22-2200002-2222-2-2-2-2-22-2-22220000-22-22000000002-2-22000000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ492-2-2-222-222-2-2200002-2-2-222-2222-2-2-22-2200002-2-220000000022-2-200000000000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ502-2-2-222-222-2-2200002-2-2-222-2222-2-2-22-2200002-2-220000000022-2-20000000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ512-2-2-222-222-2-2200002-2-2-222-22-2-2222-22-200002-2-2200000000-2-22200000000000000002-2-220000-222-2000000000000
χ522-2-2-222-222-2-2200002-2-2-222-22-2-2222-22-200002-2-2200000000-2-2220000000000000000-222-200002-2-22000000000000
χ532-2-2-222-22-222-200002-2-2-222-2222-2-2-22-220000-222-200000000-2-2220000000000002-2-2200002-2-220000000000000000
χ542-2-2-222-22-222-200002-2-2-222-2222-2-2-22-220000-222-200000000-2-222000000000000-222-20000-222-20000000000000000
χ552-2-2-222-22-222-200002-2-2-222-22-2-2222-22-20000-222-20000000022-2-20000000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ562-2-2-222-22-222-200002-2-2-222-22-2-2222-22-20000-222-20000000022-2-2000000000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ574444444444444444-1-1-1-1-1-1-1-1000000004444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ584444444444444444-1-1-1-1-1-1-1-100000000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000000000000000
χ59444444444444-4-4-4-4-1-1-1-1-1-1-1-10000000044-4-4-1-1-1-1111111110000-1-1-1-1111100000000000000000000000000000000
χ60444444444444-4-4-4-4-1-1-1-1-1-1-1-100000000-4-444-1-1-1-11111111100001111-1-1-1-100000000000000000000000000000000
χ6144444444-4-4-4-444-4-4-1-1-1-1-1-1-1-10000000000001111-1-1-1-1111100005−55−55−55−500000000000000000000000000000000
χ6244444444-4-4-4-444-4-4-1-1-1-1-1-1-1-10000000000001111-1-1-1-111110000−55−55−55−5500000000000000000000000000000000
χ6344444444-4-4-4-4-4-444-1-1-1-1-1-1-1-100000000000011111111-1-1-1-100005−55−5−55−5500000000000000000000000000000000
χ6444444444-4-4-4-4-4-444-1-1-1-1-1-1-1-100000000000011111111-1-1-1-10000−55−555−55−500000000000000000000000000000000
χ65444-4-44-4-400000000444-4-44-4-44-444-4-4-44000000000000000000000000000000000000000000000000000000000000
χ66444-4-44-4-400000000444-4-44-4-4-44-4-4444-4000000000000000000000000000000000000000000000000000000000000
χ6744-44-4-4-440000000044-44-4-4-444-44-444-4-4000000000000000000000000000000000000000000000000000000000000
χ6844-44-4-4-440000000044-44-4-4-44-44-44-4-444000000000000000000000000000000000000000000000000000000000000
χ6944-4-44-44-444-4-44i−4i4i−4i-1-111-11-11000000004-44i−4i-1-111−i−iii−i−iii0000-1-111−i−iii00000000000000000000000000000000
χ7044-4-44-44-444-4-44i−4i4i−4i-1-111-11-1100000000-44−4i4i-1-111−i−iii−i−iii000011-1-1ii−i−i00000000000000000000000000000000
χ7144-4-44-44-444-4-4−4i4i−4i4i-1-111-11-11000000004-4−4i4i-1-111ii−i−iii−i−i0000-1-111ii−i−i00000000000000000000000000000000
χ7244-4-44-44-444-4-4−4i4i−4i4i-1-111-11-1100000000-444i−4i-1-111ii−i−iii−i−i000011-1-1−i−iii00000000000000000000000000000000
χ7344-4-44-44-4-4-4444i−4i−4i4i-1-111-11-1100000000000011-1-1−i−iiiii−i−i00005−5−55i5−i5−i5i500000000000000000000000000000000
χ7444-4-44-44-4-4-4444i−4i−4i4i-1-111-11-1100000000000011-1-1−i−iiiii−i−i0000−555−5−i5i5i5−i500000000000000000000000000000000
χ7544-4-44-44-4-4-444−4i4i4i−4i-1-111-11-1100000000000011-1-1ii−i−i−i−iii00005−5−55−i5i5i5−i500000000000000000000000000000000
χ7644-4-44-44-4-4-444−4i4i4i−4i-1-111-11-1100000000000011-1-1ii−i−i−i−iii0000−555−5i5−i5−i5i500000000000000000000000000000000
χ774-44-4-4-444000000004-44-4-4-4444-4-44-444-4000000000000000000000000000000000000000000000000000000000000
χ784-44-4-4-444000000004-44-4-4-444-444-44-4-44000000000000000000000000000000000000000000000000000000000000
χ794-4-44-444-4000000004-4-44-444-44-4-4-44-444000000000000000000000000000000000000000000000000000000000000
χ804-4-44-444-4000000004-4-44-444-4-4444-44-4-4000000000000000000000000000000000000000000000000000000000000
χ81888-8-88-8-800000000-2-2-222-222000000000000000025−2525−25000000000000000000000000000000000000000000000000
χ82888-8-88-8-800000000-2-2-222-2220000000000000000−2525−2525000000000000000000000000000000000000000000000000
χ8388-88-8-8-8800000000-2-22-2222-200000000000000002i5−2i5−2i52i5000000000000000000000000000000000000000000000000
χ8488-88-8-8-8800000000-2-22-2222-20000000000000000−2i52i52i5−2i5000000000000000000000000000000000000000000000000
χ858-8888-8-8-88-88-80000-22-2-2-2222000000000000-22-220000000000000000000000000000000000000000000000000000
χ868-8888-8-8-8-88-880000-22-2-2-22220000000000002-22-20000000000000000000000000000000000000000000000000000
χ878-88-8-8-88800000000-22-2222-2-20000000000000000000025−2525−2500000000000000000000000000000000000000000000
χ888-88-8-8-88800000000-22-2222-2-200000000000000000000−2525−252500000000000000000000000000000000000000000000
χ898-8-88-888-800000000-222-22-2-22000000000000000000002i5−2i5−2i52i500000000000000000000000000000000000000000000
χ908-8-88-888-800000000-222-22-2-2200000000000000000000−2i52i52i5−2i500000000000000000000000000000000000000000000
χ918-8-8-888-888-8-880000-2222-2-22-2000000000000-222-20000000000000000000000000000000000000000000000000000
χ928-8-8-888-88-888-80000-2222-2-22-20000000000002-2-220000000000000000000000000000000000000000000000000000

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