Finite Group Databasebeta

← Group #13021281

Character table — Group #13021281

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222222244444444444888888888888101010101010101010101616161616161616161620202020202020202020202020202020202020808080808080
order12222244888845881010101010101020202020404040404040404044444488884420202020202020204888888888888888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1ii−i−i
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1−i−iii
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11−i−iii
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11ii−i−i
χ911111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11-11-11-1
χ1011111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111-1-11-11
χ1111111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-1-11-11-11
χ1211111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-111-11-1
χ1311111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-11i−i−ii
χ1411111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-11−iii−i
χ1511111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-111iiii−i−i−i−i−i−i−i−iiiii1-1−iii−i
χ1611111111-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-111−i−i−i−iiiiiiiii−i−i−i−i1-1i−i−ii
χ17222222-2-20000-22002222222-2-2-2-20000000022-2-22200000000000000-200000022-2-2000022-2-2000000
χ18222222-2-20000-22002222222-2-2-2-20000000022-2-22200000000000000-2000000-2-2220000-2-222000000
χ19222222-2-20000-22002222222-2-2-2-200000000-2-222-2-20000000000000020000002i2i−2i−2i0000−2i−2i2i2i000000
χ20222222-2-20000-22002222222-2-2-2-200000000-2-222-2-2000000000000002000000−2i−2i2i2i00002i2i−2i−2i000000
χ212222-2-2222222-22-2-2-2-2-2-22222-2-222222-2-2-2-22222-2-222220000000000-2-2-20000000000000000000000
χ222222-2-2222222-22-2-2-2-2-2-22222-2-222222-2-2-2-2-2-2-2-222-2-2-2-200000000002220000000000000000000000
χ232222-2-222-2-2-2-2-2222-2-2-2-22222-2-22-2-2-2-222222222-2-2-2-2-2-20000000000-2220000000000000000000000
χ242222-2-222-2-2-2-2-2222-2-2-2-22222-2-22-2-2-2-22222-2-2-2-222222200000000002-2-20000000000000000000000
χ252222-2-2-2-200002200-2-2-2-2222-222-20000000022-2-2-2-2000000000000002002i2i−2i−2i00002i2i−2i−2i0000000000
χ262222-2-2-2-200002200-2-2-2-2222-222-20000000022-2-2-2-200000000000000200−2i−2i2i2i0000−2i−2i2i2i0000000000
χ272222-2-2-2-200002200-2-2-2-2222-222-200000000-2-2222200000000000000-20022-2-20000-2-2220000000000
χ282222-2-2-2-200002200-2-2-2-2222-222-200000000-2-2222200000000000000-200-2-222000022-2-20000000000
χ292-22-22-200i2i2−i2−i202i2−i222-2-2-22-20000i2i2−i2−i2i2i2−i2−i22-2002-2i2i2−i2−i200000000000i2−i2i2−i2i2−i2002-2i2−i2i2−i2002-2000000
χ302-22-22-200i2i2−i2−i202i2−i222-2-2-22-20000i2i2−i2−i2i2i2−i2−i22-2002-2i2i2−i2−i200000000000i2−i2−i2i2−i2i200-22−i2i2−i2i200-22000000
χ312-22-22-200i2i2−i2−i202i2−i222-2-2-22-20000i2i2−i2−i2i2i2−i2−i2-2200-22−i2−i2i2i200000000000−i2i22−22−200−2i2i−22−22002i−2i000000
χ322-22-22-200i2i2−i2−i202i2−i222-2-2-22-20000i2i2−i2−i2i2i2−i2−i2-2200-22−i2−i2i2i200000000000−i2i2−22−22002i−2i2−22−200−2i2i000000
χ332-22-22-200−i2−i2i2i202−i2i222-2-2-22-20000−i2−i2i2i2−i2−i2i2i22-2002-2−i2−i2i2i200000000000−i2i2i2−i2i2−i200-22i2−i2i2−i200-22000000
χ342-22-22-200−i2−i2i2i202−i2i222-2-2-22-20000−i2−i2i2i2−i2−i2i2i22-2002-2−i2−i2i2i200000000000−i2i2−i2i2−i2i2002-2−i2i2−i2i2002-2000000
χ352-22-22-200−i2−i2i2i202−i2i222-2-2-22-20000−i2−i2i2i2−i2−i2i2i2-2200-22i2i2−i2−i200000000000i2−i22−22−2002i−2i−22−2200−2i2i000000
χ362-22-22-200−i2−i2i2i202−i2i222-2-2-22-20000−i2−i2i2i2−i2−i2i2i2-2200-22i2i2−i2−i200000000000i2−i2−22−2200−2i2i2−22−2002i−2i000000
χ372-22-2-2200i2i2−i2−i202−i2i2-2-222-22-20000i2i2−i2−i2−i2−i2i2i22-200-22i2i2−i2−i200000000000−i2i22−2−222i−2i002−2−222i−2i00000000
χ382-22-2-2200i2i2−i2−i202−i2i2-2-222-22-20000i2i2−i2−i2−i2−i2i2i22-200-22i2i2−i2−i200000000000−i2i2−222−2−2i2i00−222−2−2i2i00000000
χ392-22-2-2200i2i2−i2−i202−i2i2-2-222-22-20000i2i2−i2−i2−i2−i2i2i2-22002-2−i2−i2i2i200000000000i2−i2i2−i2−i2i2-2200−i2i2i2−i22-200000000
χ402-22-2-2200i2i2−i2−i202−i2i2-2-222-22-20000i2i2−i2−i2−i2−i2i2i2-22002-2−i2−i2i2i200000000000i2−i2−i2i2i2−i22-200i2−i2−i2i2-2200000000
χ412-22-2-2200−i2−i2i2i202i2−i2-2-222-22-20000−i2−i2i2i2i2i2−i2−i22-200-22−i2−i2i2i200000000000i2−i22−2−22−2i2i002−2−22−2i2i00000000
χ422-22-2-2200−i2−i2i2i202i2−i2-2-222-22-20000−i2−i2i2i2i2i2−i2−i22-200-22−i2−i2i2i200000000000i2−i2−222−22i−2i00−222−22i−2i00000000
χ432-22-2-2200−i2−i2i2i202i2−i2-2-222-22-20000−i2−i2i2i2i2i2−i2−i2-22002-2i2i2−i2−i200000000000−i2i2i2−i2−i2i22-200−i2i2i2−i2-2200000000
χ442-22-2-2200−i2−i2i2i202i2−i2-2-222-22-20000−i2−i2i2i2i2i2−i2−i2-22002-2i2i2−i2−i200000000000−i2i2−i2i2i2−i2-2200i2−i2−i2i22-200000000
χ454444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000044-1-1-1-1-1-1-1-10000000000000000000000000
χ464444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000-4-4111111110000000000000000000000000
χ4744444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-11111111100000000004-4-1-1-1-111110000000000000000000000000
χ4844444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1-1-1-1-1111111110000000000-441111-1-1-1-10000000000000000000000000
χ494444-4-4444444-4-1-4-41111-1-1-1-111-1-1-1-1-1111100000000000055−5−555−5−50000000000000000000000000
χ504444-4-4444444-4-1-4-41111-1-1-1-111-1-1-1-1-11111000000000000−5−555−5−5550000000000000000000000000
χ514444-4-444-4-4-4-4-4-1441111-1-1-1-111-11111-1-1-1-100000000000055−5−5−5−5550000000000000000000000000
χ524444-4-444-4-4-4-4-4-1441111-1-1-1-111-11111-1-1-1-1000000000000−5−55555−5−50000000000000000000000000
χ5344-4-4004-44-44-4040000004-4-4-40044-44-40000000000000000000000000000000000000000000000000
χ5444-4-4004-44-44-40-1005−55−5-11115−5-1-11-115−55−5000000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000
χ5544-4-4004-44-44-40-1005−55−5-11115−5-1-11-115−55−5000000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000
χ5644-4-4004-44-44-40-100−55−55-1111−55-1-11-11−55−55000000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000
χ5744-4-4004-44-44-40-100−55−55-1111−55-1-11-11−55−55000000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000
χ5844-4-4004-4-44-44040000004-4-4-4004-44-440000000000000000000000000000000000000000000000000
χ5944-4-4004-4-44-440-1005−55−5-11115−5-11-11-1−55−55000000000000−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000000000000000
χ6044-4-4004-4-44-440-1005−55−5-11115−5-11-11-1−55−55000000000000ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000000000000000
χ6144-4-4004-4-44-440-100−55−55-1111−55-11-11-15−55−5000000000000ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000000000000000
χ6244-4-4004-4-44-440-100−55−55-1111−55-11-11-15−55−5000000000000−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000000000000000
χ6344-4-400-440000040000004-4-4400-4000000000000004-44-400000000000000000000000000000000000
χ6444-4-400-440000040000004-4-4400-400000000000000-44-4400000000000000000000000000000000000
χ654-4-4400002i2−2i2−2i22i204000000-4-4400002i2−2i2−2i22i20000004-4002i2−2i2−2i22i200000000000000000000000000000000000
χ664-4-4400002i2−2i2−2i22i204000000-4-4400002i2−2i2−2i22i2000000-4400−2i22i22i2−2i200000000000000000000000000000000000
χ674-4-440000−2i22i22i2−2i204000000-4-440000−2i22i22i2−2i20000004-400−2i22i22i2−2i200000000000000000000000000000000000
χ684-4-440000−2i22i22i2−2i204000000-4-440000−2i22i22i2−2i2000000-44002i2−2i2−2i22i200000000000000000000000000000000000
χ69888888-8-80000-8-200-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000
χ708888-8-8-8-800008-2002222-2-2-22-2-2200000000000000000000000000000000000000000000000000000
χ7188-8-800-8800000-20025−2525−25-222-2−2525200000000000000000000000000000000000000000000000000000
χ7288-8-800-8800000-200−2525−2525-222-225−25200000000000000000000000000000000000000000000000000000
χ738-88-88-8004i24i2−4i2−4i20-24i2−4i2-2-2222-220000−i2−i2i2i2−i2−i2i2i2000000000000000000000000000000000000000000000
χ748-88-88-800−4i2−4i24i24i20-2−4i24i2-2-2222-220000i2i2−i2−i2i2i2−i2−i2000000000000000000000000000000000000000000000
χ758-88-8-88004i24i2−4i2−4i20-2−4i24i222-2-22-220000−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000000000000
χ768-88-8-8800−4i2−4i24i24i20-24i2−4i222-2-22-220000i2i2−i2−i2−i2−i2i2i2000000000000000000000000000000000000000000000
χ778-8-8800004i2−4i2−4i24i20-20025−25−252522-20000−i2i2i2−i2i10−i10−i10i10000000000000000000000000000000000000000000000
χ788-8-8800004i2−4i2−4i24i20-200−252525−2522-20000−i2i2i2−i2−i10i10i10−i10000000000000000000000000000000000000000000000
χ798-8-880000−4i24i24i2−4i20-20025−25−252522-20000i2−i2−i2i2−i10i10i10−i10000000000000000000000000000000000000000000000
χ808-8-880000−4i24i24i2−4i20-200−252525−2522-20000i2−i2−i2i2i10−i10−i10i10000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.