Finite Group Databasebeta

← Group #14279542

Character table — Group #14279542

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222244444444444444444444488888888888888888816161616161616161616161616161620202020202020202020202040408080240240240240
order1223666444510101012121212121215153030303030302020202020206060606060606060606060604121220202020606060606060606088882424242424242424246124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i
χ41111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1i−i−ii
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−iii−i
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ92222222-2-222222-2-2-2-2222222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000002-22-20000
χ102222222-2-222222-2-2-2-2222222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000-22-220000
χ11222-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-10000
χ12222-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2110000
χ13222-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2110000
χ14222-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-2-2-211111111-2-2-2-21111111122-1-10000
χ15222-1-1-1-1-2-2222221111-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111110−i3i30000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i32-2-110000
χ16222-1-1-1-1-2-2222221111-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111110−i3i30000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-221-10000
χ17222-1-1-1-1-2-2222221111-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111110i3−i30000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-221-10000
χ18222-1-1-1-1-2-2222221111-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111110i3−i30000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i32-2-110000
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χ254444444444-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-411111111111100000000000000000000
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χ33444-2-2-2-200-4-1-1-1-1−2i3−2i32i32i3221+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521155−5−5−1+i152−1+i152−1−i152−1−i152ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116000−ζ4−ζ28−ζ44+ζ52−ζ68+ζ76+ζ92+ζ116ζ4+ζ28+ζ44−ζ52+ζ68−ζ76−ζ92−ζ116ζ4−ζ28+ζ44+ζ52−ζ68−ζ76+ζ92−ζ116−ζ4+ζ28−ζ44−ζ52+ζ68+ζ76−ζ92+ζ116ζ28+ζ44−ζ52−ζ116−ζ28−ζ44+ζ52+ζ116−ζ4+ζ68+ζ76−ζ92ζ4−ζ68−ζ76+ζ92ζ4+ζ68−ζ76−ζ92−ζ4−ζ68+ζ76+ζ92ζ28−ζ44−ζ52+ζ116−ζ28+ζ44+ζ52−ζ11600000000000000000000
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χ6488-88-8-88000-2-222000000-2-2-2-22222−25250000−252525−250000000000000000000000000000000000000000000
χ6588-88-8-88000-2-222000000-2-2-2-2222225−25000025−25−25250000000000000000000000000000000000000000000
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χ6788-8-444-4000-2-2220000−4i34i31+i151−i151+i151−i15−1−i15−1−i15−1+i15−1+i1525−2500002ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ1162ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ920000000000000000000000000000000000000000000
χ6888-8-444-4000-2-22200004i3−4i31−i151+i151−i151+i15−1+i15−1+i15−1−i15−1−i1525−250000−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ1160000000000000000000000000000000000000000000
χ6988-8-444-4000-2-22200004i3−4i31+i151−i151+i151−i15−1−i15−1−i15−1+i15−1+i15−25250000−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ920000000000000000000000000000000000000000000
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χ728-80800-8−4i4i0-22−2525−4i4i−4i4i00-2-222−252525−25002ζ22+2ζ38+2ζ62+2ζ118−2ζ22−2ζ38−2ζ62−2ζ1182ζ14+2ζ46+2ζ86+2ζ94−2ζ14−2ζ46−2ζ86−2ζ9400002ζ22+2ζ38+2ζ62+2ζ118−2ζ22−2ζ38−2ζ62−2ζ1182ζ22+2ζ38+2ζ62+2ζ118−2ζ22−2ζ38−2ζ62−2ζ1182ζ14+2ζ46+2ζ86+2ζ94−2ζ14−2ζ46−2ζ86−2ζ942ζ14+2ζ46+2ζ86+2ζ94−2ζ14−2ζ46−2ζ86−2ζ9400000000000000000000000000000000000
χ738-80800-8−4i4i0-2225−25−4i4i−4i4i00-2-22225−25−2525002ζ14+2ζ46+2ζ86+2ζ94−2ζ14−2ζ46−2ζ86−2ζ942ζ22+2ζ38+2ζ62+2ζ118−2ζ22−2ζ38−2ζ62−2ζ11800002ζ14+2ζ46+2ζ86+2ζ94−2ζ14−2ζ46−2ζ86−2ζ942ζ14+2ζ46+2ζ86+2ζ94−2ζ14−2ζ46−2ζ86−2ζ942ζ22+2ζ38+2ζ62+2ζ118−2ζ22−2ζ38−2ζ62−2ζ1182ζ22+2ζ38+2ζ62+2ζ118−2ζ22−2ζ38−2ζ62−2ζ11800000000000000000000000000000000000
χ748-80-4−4i34i344i−4i0-22−2525−4ζ22−4ζ46−4ζ94−4ζ1184ζ22+4ζ46+4ζ94+4ζ118−4ζ14−4ζ38−4ζ62−4ζ864ζ14+4ζ38+4ζ62+4ζ86001+i151−i15−1−i15−1+i152ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ922ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ11600−2ζ22−2ζ38−2ζ62−2ζ1182ζ22+2ζ38+2ζ62+2ζ118−2ζ14−2ζ46−2ζ86−2ζ942ζ14+2ζ46+2ζ86+2ζ9400002ζ22+2ζ118−2ζ22−2ζ1182ζ38+2ζ62−2ζ38−2ζ622ζ46+2ζ94−2ζ46−2ζ942ζ14+2ζ86−2ζ14−2ζ8600000000000000000000000000000000000
χ758-80-4−4i34i344i−4i0-2225−25−4ζ22−4ζ46−4ζ94−4ζ1184ζ22+4ζ46+4ζ94+4ζ118−4ζ14−4ζ38−4ζ62−4ζ864ζ14+4ζ38+4ζ62+4ζ86001−i151+i15−1+i15−1−i152ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ1162ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ9200−2ζ14−2ζ46−2ζ86−2ζ942ζ14+2ζ46+2ζ86+2ζ94−2ζ22−2ζ38−2ζ62−2ζ1182ζ22+2ζ38+2ζ62+2ζ11800002ζ46+2ζ94−2ζ46−2ζ942ζ14+2ζ86−2ζ14−2ζ862ζ22+2ζ118−2ζ22−2ζ1182ζ38+2ζ62−2ζ38−2ζ6200000000000000000000000000000000000
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χ778-80-4−4i34i34−4i4i0-2225−254ζ22+4ζ46+4ζ94+4ζ118−4ζ22−4ζ46−4ζ94−4ζ1184ζ14+4ζ38+4ζ62+4ζ86−4ζ14−4ζ38−4ζ62−4ζ86001−i151+i15−1+i15−1−i152ζ28−2ζ44+2ζ52−2ζ116−2ζ28+2ζ44−2ζ52+2ζ1162ζ4−2ζ68+2ζ76−2ζ92−2ζ4+2ζ68−2ζ76+2ζ92002ζ14+2ζ46+2ζ86+2ζ94−2ζ14−2ζ46−2ζ86−2ζ942ζ22+2ζ38+2ζ62+2ζ118−2ζ22−2ζ38−2ζ62−2ζ1180000−2ζ46−2ζ942ζ46+2ζ94−2ζ14−2ζ862ζ14+2ζ86−2ζ22−2ζ1182ζ22+2ζ118−2ζ38−2ζ622ζ38+2ζ6200000000000000000000000000000000000
χ788-80-44i3−4i344i−4i0-22−2525−4ζ14−4ζ38−4ζ62−4ζ864ζ14+4ζ38+4ζ62+4ζ86−4ζ22−4ζ46−4ζ94−4ζ1184ζ22+4ζ46+4ζ94+4ζ118001−i151+i15−1+i15−1−i15−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ9200−2ζ22−2ζ38−2ζ62−2ζ1182ζ22+2ζ38+2ζ62+2ζ118−2ζ14−2ζ46−2ζ86−2ζ942ζ14+2ζ46+2ζ86+2ζ9400002ζ38+2ζ62−2ζ38−2ζ622ζ22+2ζ118−2ζ22−2ζ1182ζ14+2ζ86−2ζ14−2ζ862ζ46+2ζ94−2ζ46−2ζ9400000000000000000000000000000000000
χ798-80-44i3−4i344i−4i0-2225−25−4ζ14−4ζ38−4ζ62−4ζ864ζ14+4ζ38+4ζ62+4ζ86−4ζ22−4ζ46−4ζ94−4ζ1184ζ22+4ζ46+4ζ94+4ζ118001+i151−i15−1−i15−1+i15−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ11600−2ζ14−2ζ46−2ζ86−2ζ942ζ14+2ζ46+2ζ86+2ζ94−2ζ22−2ζ38−2ζ62−2ζ1182ζ22+2ζ38+2ζ62+2ζ11800002ζ14+2ζ86−2ζ14−2ζ862ζ46+2ζ94−2ζ46−2ζ942ζ38+2ζ62−2ζ38−2ζ622ζ22+2ζ118−2ζ22−2ζ11800000000000000000000000000000000000
χ808-80-44i3−4i34−4i4i0-22−25254ζ14+4ζ38+4ζ62+4ζ86−4ζ14−4ζ38−4ζ62−4ζ864ζ22+4ζ46+4ζ94+4ζ118−4ζ22−4ζ46−4ζ94−4ζ118001−i151+i15−1+i15−1−i15−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ116−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92002ζ22+2ζ38+2ζ62+2ζ118−2ζ22−2ζ38−2ζ62−2ζ1182ζ14+2ζ46+2ζ86+2ζ94−2ζ14−2ζ46−2ζ86−2ζ940000−2ζ38−2ζ622ζ38+2ζ62−2ζ22−2ζ1182ζ22+2ζ118−2ζ14−2ζ862ζ14+2ζ86−2ζ46−2ζ942ζ46+2ζ9400000000000000000000000000000000000
χ818-80-44i3−4i34−4i4i0-2225−254ζ14+4ζ38+4ζ62+4ζ86−4ζ14−4ζ38−4ζ62−4ζ864ζ22+4ζ46+4ζ94+4ζ118−4ζ22−4ζ46−4ζ94−4ζ118001+i151−i15−1−i15−1+i15−2ζ4+2ζ68−2ζ76+2ζ922ζ4−2ζ68+2ζ76−2ζ92−2ζ28+2ζ44−2ζ52+2ζ1162ζ28−2ζ44+2ζ52−2ζ116002ζ14+2ζ46+2ζ86+2ζ94−2ζ14−2ζ46−2ζ86−2ζ942ζ22+2ζ38+2ζ62+2ζ118−2ζ22−2ζ38−2ζ62−2ζ1180000−2ζ14−2ζ862ζ14+2ζ86−2ζ46−2ζ942ζ46+2ζ94−2ζ38−2ζ622ζ38+2ζ62−2ζ22−2ζ1182ζ22+2ζ11800000000000000000000000000000000000

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