Finite Group Databasebeta

← Group #13017507

Character table — Group #13017507

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111444444444444448888888888888888101010101010101010101010161616161616161620204040404040404040404040404040404040404040
order12222222444444510101010101010444420202020202020202020202022224444444420202020202020204422444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ51111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-2-2-2222222220000-2-2-2-22222-2-2-2-222222222-2-2-2-200000000-2-200000000000000000000
χ182222222222-2-2-2-2222222220000-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000002200000000000000000000
χ1922222222-2-222-2-2222222220000-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000002200000000000000000000
χ2022222222-2-222-2-2222222220000-2-2-2-2-2-2-2-22222-2-2-2-22222222200000000-2-200000000000000000000
χ21222-2-22-2-2002i−2i00222-2-2-22-20000000000002i2i−2i−2i000022-2-22i2i−2i−2i000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ22222-2-22-2-2002i−2i00222-2-2-22-20000000000002i2i−2i−2i000022-2-22i2i−2i−2i00000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ23222-2-22-2-2002i−2i00222-2-2-22-20000000000002i2i−2i−2i0000-2-222−2i−2i2i2i000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ24222-2-22-2-2002i−2i00222-2-2-22-20000000000002i2i−2i−2i0000-2-222−2i−2i2i2i00000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ25222-2-22-2-200−2i2i00222-2-2-22-2000000000000−2i−2i2i2i000022-2-2−2i−2i2i2i000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ26222-2-22-2-200−2i2i00222-2-2-22-2000000000000−2i−2i2i2i000022-2-2−2i−2i2i2i00000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ27222-2-22-2-200−2i2i00222-2-2-22-2000000000000−2i−2i2i2i0000-2-2222i2i−2i−2i000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ28222-2-22-2-200−2i2i00222-2-2-22-2000000000000−2i−2i2i2i0000-2-2222i2i−2i−2i00000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ2922-22-2-22-22i−2i000022-22-2-2-22000000002i2i−2i−2i00002-22-22i−2i2i−2i000000000000000000000000002−2i2−i22−2i2−i2
χ3022-22-2-22-22i−2i000022-22-2-2-22000000002i2i−2i−2i00002-22-22i−2i2i−2i00000000000000000000000000−22−i2i2−22−i2i2
χ3122-22-2-22-22i−2i000022-22-2-2-22000000002i2i−2i−2i0000-22-22−2i2i−2i2i00000000000000000000000000i2−i2−22−i2i22−2
χ3222-22-2-22-22i−2i000022-22-2-2-22000000002i2i−2i−2i0000-22-22−2i2i−2i2i00000000000000000000000000−i2i22−2i2−i2−22
χ3322-22-2-22-2−2i2i000022-22-2-2-2200000000−2i−2i2i2i00002-22-2−2i2i−2i2i000000000000000000000000002−2−i2i22−2−i2i2
χ3422-22-2-22-2−2i2i000022-22-2-2-2200000000−2i−2i2i2i00002-22-2−2i2i−2i2i00000000000000000000000000−22i2−i2−22i2−i2
χ3522-22-2-22-2−2i2i000022-22-2-2-2200000000−2i−2i2i2i0000-22-222i−2i2i−2i00000000000000000000000000i2−i22−2−i2i2−22
χ3622-22-2-22-2−2i2i000022-22-2-2-2200000000−2i−2i2i2i0000-22-222i−2i2i−2i00000000000000000000000000−i2i2−22i2−i22−2
χ372-2-2-2-222200002-22-2-2-2-2222002-222-2-2000000002-2-2200002-22-2000022-2-200002-20000000000000000
χ382-2-2-2-222200002-22-2-2-2-2222002-222-2-200000000-222-20000-22-22000022-2-20000-220000000000000000
χ392-2-2-2-222200002-22-2-2-2-222200-2222-2-2000000002-2-2200002-22-20000-2-2220000-220000000000000000
χ402-2-2-2-222200002-22-2-2-2-222200-2222-2-200000000-222-20000-22-220000-2-22200002-20000000000000000
χ412-2-2-2-22220000-222-2-2-2-22222-200-2-222000000002-2-220000-22-2222-2-20000002-2000000000000000000
χ422-2-2-2-22220000-222-2-2-2-22222-200-2-22200000000-222-200002-22-222-2-2000000-22000000000000000000
χ432-2-2-2-22220000-222-2-2-2-2222-2200-2-222000000002-2-220000-22-22-2-222000000-22000000000000000000
χ442-2-2-2-22220000-222-2-2-2-2222-2200-2-22200000000-222-200002-22-2-2-2220000002-2000000000000000000
χ4544444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-10000000000000000000000
χ4644444444444444-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111110000000000000000000000
χ474444444444-4-4-4-4-1-1-1-1-1-1-1-100001111-1-1-1-111110000000000005−55−55−55−50000000000000000000000
χ484444444444-4-4-4-4-1-1-1-1-1-1-1-100001111-1-1-1-11111000000000000−55−55−55−550000000000000000000000
χ4944444444-4-444-4-4-1-1-1-1-1-1-1-1000011111111-1-1-1-10000000000005−55−5−55−550000000000000000000000
χ5044444444-4-444-4-4-1-1-1-1-1-1-1-1000011111111-1-1-1-1000000000000−55−555−55−50000000000000000000000
χ5144444444-4-4-4-444-1-1-1-1-1-1-1-144-4-4-1-1-1-111111111000000000000-1-1-1-111110000000000000000000000
χ5244444444-4-4-4-444-1-1-1-1-1-1-1-1-4-444-1-1-1-1111111110000000000001111-1-1-1-10000000000000000000000
χ5344-4-44-4-4400000044-4-444-4-4000000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ5444-4-44-4-4400000044-4-444-4-400000000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ554-444-4-4-440000004-444-44-4-40000000000000000000000000000000000004i−4i00000000000000000000
χ564-444-4-4-440000004-444-44-4-4000000000000000000000000000000000000−4i4i00000000000000000000
χ574-44-44-44-40000004-44-44-4-44000000000000000044-4-400000000000000000000000000000000000000
χ584-44-44-44-40000004-44-44-4-440000000000000000-4-44400000000000000000000000000000000000000
χ594-4-4444-4-40000004-4-444-44-40000000000000000000000004i−4i−4i4i000000000000000000000000000000
χ604-4-4444-4-40000004-4-444-44-4000000000000000000000000−4i4i4i−4i000000000000000000000000000000
χ614-4-4-4-444400004-4-11111-1-1-1004-4-1-1115−55−55−55−50000000000005−5−55-1-1110000000000000000000000
χ624-4-4-4-444400004-4-11111-1-1-1004-4-1-111−55−55−55−55000000000000−555−5-1-1110000000000000000000000
χ634-4-4-4-444400004-4-11111-1-1-100-44-1-1115−55−55−55−5000000000000−555−511-1-10000000000000000000000
χ644-4-4-4-444400004-4-11111-1-1-100-44-1-111−55−55−55−550000000000005−5−5511-1-10000000000000000000000
χ654-4-4-4-44440000-44-11111-1-1-14-40011-1-15−55−5−55−55000000000000-1-1115−5−550000000000000000000000
χ664-4-4-4-44440000-44-11111-1-1-14-40011-1-1−55−555−55−5000000000000-1-111−555−50000000000000000000000
χ674-4-4-4-44440000-44-11111-1-1-1-440011-1-15−55−5−55−5500000000000011-1-1−555−50000000000000000000000
χ684-4-4-4-44440000-44-11111-1-1-1-440011-1-1−55−555−55−500000000000011-1-15−5−550000000000000000000000
χ69888-8-88-8-8008i−8i00-2-2-2222-22000000000000−2i−2i2i2i000000000000000000000000000000000000000000
χ70888-8-88-8-800−8i8i00-2-2-2222-220000000000002i2i−2i−2i000000000000000000000000000000000000000000
χ7188-88-8-88-88i−8i0000-2-22-2222-200000000−2i−2i2i2i0000000000000000000000000000000000000000000000
χ7288-88-8-88-8−8i8i0000-2-22-2222-2000000002i2i−2i−2i0000000000000000000000000000000000000000000000
χ7388-8-88-8-88000000-2-222-2-222000025−2525−2500000000000000000000000000000000000000000000000000
χ7488-8-88-8-88000000-2-222-2-2220000−2525−252500000000000000000000000000000000000000000000000000
χ758-888-8-8-88000000-22-2-22-222000025−25−252500000000000000000000000000000000000000000000000000
χ768-888-8-8-88000000-22-2-22-2220000−252525−2500000000000000000000000000000000000000000000000000
χ778-88-88-88-8000000-22-22-222-2000000002i5−2i5−2i52i50000000000000000000000000000000000000000000000
χ788-88-88-88-8000000-22-22-222-200000000−2i52i52i5−2i50000000000000000000000000000000000000000000000
χ798-8-8888-8-8000000-222-2-22-220000000000002i5−2i5−2i52i5000000000000000000000000000000000000000000
χ808-8-8888-8-8000000-222-2-22-22000000000000−2i52i52i5−2i5000000000000000000000000000000000000000000

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