Finite Group Databasebeta

← Group #13086310

Character table — Group #13086310

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112222222224444444444444444444444444444444558888888888888888888888888881010101010101010102020202020202020202020202090909090180180
order1233334666625666666661012121212151515151515151530303030303030302210102030303030303030303030303030303030606060606060606046666666626666666612121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−i
χ4111111111111111111111111111111111111111111-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii
χ511111111111-11-1-1-1-1-1-1-1-111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-111111111-1-1
χ611111111111-11-1-1-1-1-1-1-1-111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111-11-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111111-1-1-1-1ii−i−i−ii
χ811111111111-11-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111111-1-1-1-1−i−iiii−i
χ9222222-2222202000000002-2-2-2-222222222222222222200-20000000000000000-2-2-2-2-2-2-2-2-222222222000000000-2-2-2-2000000
χ10222222-2222202000000002-2-2-2-22222222222222222-2-200-20000000000000000-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-20000000002222000000
χ11222-1-1-122-1-1-12222-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-12-1-1-1000000
χ12222-1-1-122-1-1-12222-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-22222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2111111-2-2-2111111-2111000000
χ13222-1-1-122-1-1-1-22-2-211111122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-2-22-2-2-2-211111111111122-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-21111112-1-1-1000000
χ14222-1-1-122-1-1-1-22-2-211111122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-22-2-2-2-211111111111122-1-1-1-1-1-1-2-2-2111111222-1-1-1-1-1-1-2111000000
χ15222-1-1-1-22-1-1-10200−i3−i3−i3i3i3i32-211122-1-1-1-1-1-122-1-1-1-1-1-12200-20000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-2111111-222-1-1-1-1-1-1000−i3−i3−i3i3i3i3-2111000000
χ16222-1-1-1-22-1-1-10200−i3−i3−i3i3i3i32-211122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-20000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-21111112-2-2111111000i3i3i3−i3−i3−i32-1-1-1000000
χ17222-1-1-1-22-1-1-10200i3i3i3−i3−i3−i32-211122-1-1-1-1-1-122-1-1-1-1-1-12200-20000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-2111111-222-1-1-1-1-1-1000i3i3i3−i3−i3−i3-2111000000
χ18222-1-1-1-22-1-1-10200i3i3i3−i3−i3−i32-211122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-20000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-21111112-2-2111111000−i3−i3−i3i3i3i32-1-1-1000000
χ1922-12-1-12-12-1-122-1-12-1-12-1-12-12-1-1-1-122-1-1-1-1-1-122-1-1-1-122222-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-122-1-1-1-12-1-12-1-12-1-1-12-1-1000000
χ2022-12-1-12-12-1-122-1-12-1-12-1-12-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-2222-1-1-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-211-2-21111-211-211-2111-211000000
χ2122-12-1-12-12-1-1-2211-211-2112-12-1-1-1-122-1-1-1-1-1-122-1-1-1-122-2-221111-2-21111-2-21111-1-122-1-1-1-12-1-122-1-1-1-1-211-211-211-12-1-1000000
χ2222-12-1-12-12-1-1-2211-211-2112-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-221111-2-21111-2-21111-1-122-1-1-1-1-211-2-211112-1-12-1-12-1-11-211000000
χ2322-12-1-1-2-12-1-102−i3i30−i3i30−i3i321-211-1-122-1-1-1-1-1-122-1-1-1-12200-2−i3−i3i3i300−i3−i3i3i300−i3−i3i3i311-2-21111-2-1-122-1-1-1-10−i3i30−i3i30−i3i31-211000000
χ2422-12-1-1-2-12-1-102−i3i30−i3i30−i3i321-211-1-122-1-1-1-1-1-122-1-1-1-1-2-200-2−i3−i3i3i300−i3−i3i3i300−i3−i3i3i311-2-21111211-2-211110i3−i30i3−i30i3−i3-12-1-1000000
χ2522-12-1-1-2-12-1-102i3−i30i3−i30i3−i321-211-1-122-1-1-1-1-1-122-1-1-1-12200-2i3i3−i3−i300i3i3−i3−i300i3i3−i3−i311-2-21111-2-1-122-1-1-1-10i3−i30i3−i30i3−i31-211000000
χ2622-12-1-1-2-12-1-102i3−i30i3−i30i3−i321-211-1-122-1-1-1-1-1-122-1-1-1-1-2-200-2i3i3−i3−i300i3i3−i3−i300i3i3−i3−i311-2-21111211-2-211110−i3i30−i3i30−i3i3-12-1-1000000
χ2722-1-12-12-1-12-122-1-1-12-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-122222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-12-1-1-1-122-1-12-1-1-12-1-1-12-1-12-1000000
χ2822-1-12-12-1-12-122-1-1-12-1-1-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-2-2222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-21111-2-211-2111-2111-211-21000000
χ2922-1-12-12-1-12-1-22111-2111-22-1-12-1-1-1-1-122-1-1-1-1-1-122-1-122-2-22111111-2-2111111-2-2-1-1-1-122-1-12-1-1-1-122-1-1-2111-2111-2-1-12-1000000
χ3022-1-12-12-1-12-1-22111-2111-22-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-2-2-2-22111111-2-2111111-2-2-1-1-1-122-1-1-21111-2-2112-1-1-12-1-1-1211-21000000
χ3122-1-12-1-2-1-12-102−i3i3i30−i3−i3i30211-21-1-1-1-122-1-1-1-1-1-122-1-12200-2−i3−i3i3i3i3i300−i3−i3−i3−i3i3i3001111-2-211-2-1-1-1-122-1-10−i3i3i30−i3−i3i3011-21000000
χ3222-1-12-1-2-1-12-102−i3i3i30−i3−i3i30211-21-1-1-1-122-1-1-1-1-1-122-1-1-2-200-2−i3−i3i3i3i3i300−i3−i3−i3−i3i3i3001111-2-21121111-2-2110i3−i3−i30i3i3−i30-1-12-1000000
χ3322-1-12-1-2-1-12-102i3−i3−i30i3i3−i30211-21-1-1-1-122-1-1-1-1-1-122-1-12200-2i3i3−i3−i3−i3−i300i3i3i3i3−i3−i3001111-2-211-2-1-1-1-122-1-10i3−i3−i30i3i3−i3011-21000000
χ3422-1-12-1-2-1-12-102i3−i3−i30i3i3−i30211-21-1-1-1-122-1-1-1-1-1-122-1-1-2-200-2i3i3−i3−i3−i3−i300i3i3i3i3−i3−i3001111-2-21121111-2-2110−i3i3i30−i3−i3i30-1-12-1000000
χ3522-1-1-122-1-1-1222-1-1-1-12-12-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1-1-12-12-1-1-1-12000000
χ3622-1-1-122-1-1-1222-1-1-1-12-12-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-2-2222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-2111111-2-2-21111-21-21111-2000000
χ3722-1-1-122-1-1-12-221111-21-212-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-2-2211111111-2-211-2-211-1-1-1-1-1-1222-1-1-1-1-1-122-21111-21-21-1-1-12000000
χ3822-1-1-122-1-1-12-221111-21-212-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-2-2-2-2211111111-2-211-2-211-1-1-1-1-1-122-2111111-2-22-1-1-1-12-12-1111-2000000
χ3922-1-1-12-2-1-1-1202−i3i3−i3i30i30−i32111-2-1-1-1-1-1-122-1-1-1-1-1-1222200-2−i3−i3i3i3−i3−i3i3i300i3i300−i3−i3111111-2-2-2-1-1-1-1-1-1220−i3i3−i3i30i30−i3111-2000000
χ4022-1-1-12-2-1-1-1202−i3i3−i3i30i30−i32111-2-1-1-1-1-1-122-1-1-1-1-1-122-2-200-2−i3−i3i3i3−i3−i3i3i300i3i300−i3−i3111111-2-22111111-2-20i3−i3i3−i30−i30i3-1-1-12000000
χ4122-1-1-12-2-1-1-1202i3−i3i3−i30−i30i32111-2-1-1-1-1-1-122-1-1-1-1-1-1222200-2i3i3−i3−i3i3i3−i3−i300−i3−i300i3i3111111-2-2-2-1-1-1-1-1-1220i3−i3i3−i30−i30i3111-2000000
χ4222-1-1-12-2-1-1-1202i3−i3i3−i30−i30i32111-2-1-1-1-1-1-122-1-1-1-1-1-122-2-200-2i3i3−i3−i3i3i3−i3−i300−i3−i300i3i3111111-2-22111111-2-20−i3i3−i3i30i30−i3-1-1-12000000
χ432-222220-2-2-2-20200000000-2000022222222-2-2-2-2-2-2-2-22-200000000000000000000000000002-22-22-22-20000000000000−i2i2−i2i200
χ442-222220-2-2-2-20200000000-2000022222222-2-2-2-2-2-2-2-22-200000000000000000000000000002-22-22-22-20000000000000i2−i2i2−i200
χ452-222220-2-2-2-20200000000-2000022222222-2-2-2-2-2-2-2-2-220000000000000000000000000000-22-22-22-2200000000000002−2−2200
χ462-222220-2-2-2-20200000000-2000022222222-2-2-2-2-2-2-2-2-220000000000000000000000000000-22-22-22-220000000000000−222−200
χ47444444444444-144444444-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000
χ4844444444444-4-1-4-4-4-4-4-4-4-4-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10011-11111111111111111-1-1-1-1-1-1-1-10000000000000000000000000000
χ49444444-444440-100000000-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100−551−55−55−55−55−55−55−55−55111111110000000000000000000000000000
χ50444444-444440-100000000-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1005−515−55−55−55−55−55−55−55−5111111110000000000000000000000000000
χ51444-2-2-244-2-2-24-144-2-2-2-2-2-2-14-2-2-2-1-11−i1521+i1521−i1521+i1521−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i15200-1-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521+i1521−i1521+i1521−i152-1-11−i1521+i1521−i1521+i1521−i1521+i1520000000000000000000000000000
χ52444-2-2-244-2-2-24-144-2-2-2-2-2-2-14-2-2-2-1-11+i1521−i1521+i1521−i1521+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i15200-1-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521−i1521+i1521−i1521+i152-1-11+i1521−i1521+i1521−i1521+i1521−i1520000000000000000000000000000
χ53444-2-2-244-2-2-2-4-1-4-4222222-14-2-2-2-1-11−i1521+i1521−i1521+i1521−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i1520011-11111−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152-1-11−i1521+i1521−i1521+i1521−i1521+i1520000000000000000000000000000
χ54444-2-2-244-2-2-2-4-1-4-4222222-14-2-2-2-1-11+i1521−i1521+i1521−i1521+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i1520011-11111−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152-1-11+i1521−i1521+i1521−i1521+i1521−i1520000000000000000000000000000
χ55444-2-2-2-44-2-2-20-100−2i3−2i3−2i32i32i32i3-1-4222-1-11−i1521+i1521−i1521+i1521−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i152005−515−55−5ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ11611−1+i152−1−i152−1+i152−1−i152−1+i152−1−i1520000000000000000000000000000
χ56444-2-2-2-44-2-2-20-100−2i3−2i3−2i32i32i32i3-1-4222-1-11+i1521−i1521+i1521−i1521+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i15200−551−55−55ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ9211−1−i152−1+i152−1−i152−1+i152−1−i152−1+i1520000000000000000000000000000
χ57444-2-2-2-44-2-2-20-1002i32i32i3−2i3−2i3−2i3-1-4222-1-11−i1521+i1521−i1521+i1521−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i15200−551−55−55−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ11611−1+i152−1−i152−1+i152−1−i152−1+i152−1−i1520000000000000000000000000000
χ58444-2-2-2-44-2-2-20-1002i32i32i3−2i3−2i3−2i3-1-4222-1-11+i1521−i1521+i1521−i1521+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i152005−515−55−5−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ9211−1−i152−1+i152−1−i152−1+i152−1−i152−1+i1520000000000000000000000000000
χ5944-24-2-24-24-2-24-1-2-24-2-24-2-2-1-24-2-21−i1521+i152-1-11−i1521+i1521+i1521−i1521−i1521+i152-1-11−i1521+i1521+i1521−i15200-1-1-11−i1521+i1521+i1521−i152-1-11−i1521+i1521+i1521−i152-1-11−i1521+i1521+i1521−i1521−i1521+i152-1-11−i1521+i1521+i1521−i1520000000000000000000000000000
χ6044-24-2-24-24-2-24-1-2-24-2-24-2-2-1-24-2-21+i1521−i152-1-11+i1521−i1521−i1521+i1521+i1521−i152-1-11+i1521−i1521−i1521+i15200-1-1-11+i1521−i1521−i1521+i152-1-11+i1521−i1521−i1521+i152-1-11+i1521−i1521−i1521+i1521+i1521−i152-1-11+i1521−i1521−i1521+i1520000000000000000000000000000
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χ6244-24-2-24-24-2-2-4-122-422-422-1-24-2-21+i1521−i152-1-11+i1521−i1521−i1521+i1521+i1521−i152-1-11+i1521−i1521−i1521+i1520011-1−1−i152−1+i152−1+i152−1−i15211−1−i152−1+i152−1+i152−1−i15211−1−i152−1+i152−1+i152−1−i1521+i1521−i152-1-11+i1521−i1521−i1521+i1520000000000000000000000000000
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χ998-8-4-4-480444-80-200000000200001+i151−i151+i151−i151−i151+i15-2-2−1−i15−1+i15−1−i15−1+i15−1+i15−1−i1522000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.