Finite Group Databasebeta

← Group #14512442

Character table — Group #14512442

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111224444444455556688888888101012161616161616161616161616161616162424242430304040404040404040606060606060606060120120120120
order12224451010102020202044444436661212121244415153030303030306060606060606060202020204412121212121212122888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111-1-1-1-11111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ411111111111111-1-1-1-11111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ51111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-111-1-11-11-1
χ61111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-111-11-11
χ71111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111ii−i−i−i−iiii−i−ii
χ81111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111−i−iiiii−i−i−iii−i
χ922222222222222222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12000000000000
χ1022222222222222-2-2-2-222-1-1-1-1-1-1-1-1-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-211111111-2000000000000
χ112222-2-22222-2-2-2-2222222-1-1-1-11111-2-2-2-1-1-1-1-1-1-1-11111111122-2-222-1-1-1-11111-2000000000000
χ122222-2-22222-2-2-2-2-2-2-2-222-1-1-1-1111122-2-1-1-1-1-1-1-1-11111111122-2-2-2-21111-1-1-1-12000000000000
χ1322-2-2002-22-200002i2i−2i−2i2-22-22-200000002222-2-2-2-2000000002-2002i−2i2i2i−2i−2i00000000000000000
χ1422-2-2002-22-200002i2i−2i−2i2-2-11-1133−3−3000-1-1-1-111113333−3−3−3−32-2002i−2i−i−iii−i3−i3i3i30000000000000
χ1522-2-2002-22-200002i2i−2i−2i2-2-11-11−3−333000-1-1-1-11111−3−3−3−333332-2002i−2i−i−iiii3i3−i3−i30000000000000
χ1622-2-2002-22-20000−2i−2i2i2i2-22-22-200000002222-2-2-2-2000000002-200−2i2i−2i−2i2i2i00000000000000000
χ1722-2-2002-22-20000−2i−2i2i2i2-2-11-1133−3−3000-1-1-1-111113333−3−3−3−32-200−2i2iii−i−ii3i3−i3−i30000000000000
χ1822-2-2002-22-20000−2i−2i2i2i2-2-11-11−3−333000-1-1-1-11111−3−3−3−333332-200−2i2iii−i−i−i3−i3i3i30000000000000
χ192-22-22i−2i2-2-222i2i−2i−2i2-22-200-111-1i−ii−i2i−2i0-1-111-1-111ii−i−iii−i−i0000001-11-1i−ii−i02−2−i2i22−2−i2i20000
χ202-22-22i−2i2-2-222i2i−2i−2i2-22-200-111-1i−ii−i2i−2i0-1-111-1-111ii−i−iii−i−i0000001-11-1i−ii−i0−22i2−i2−22i2−i20000
χ212-22-22i−2i2-2-222i2i−2i−2i-22-2200-111-1i−ii−i−2i2i0-1-111-1-111ii−i−iii−i−i000000-11-11−ii−ii0−i2i2−22i2−i22−20000
χ222-22-22i−2i2-2-222i2i−2i−2i-22-2200-111-1i−ii−i−2i2i0-1-111-1-111ii−i−iii−i−i000000-11-11−ii−ii0i2−i22−2−i2i2−220000
χ232-22-2−2i2i2-2-22−2i−2i2i2i2-22-200-111-1−ii−ii−2i2i0-1-111-1-111−i−iii−i−iii0000001-11-1−ii−ii02−2i2−i22−2i2−i20000
χ242-22-2−2i2i2-2-22−2i−2i2i2i2-22-200-111-1−ii−ii−2i2i0-1-111-1-111−i−iii−i−iii0000001-11-1−ii−ii0−22−i2i2−22−i2i20000
χ252-22-2−2i2i2-2-22−2i−2i2i2i-22-2200-111-1−ii−ii2i−2i0-1-111-1-111−i−iii−i−iii000000-11-11i−ii−i0−i2i22−2i2−i2−220000
χ262-22-2−2i2i2-2-22−2i−2i2i2i-22-2200-111-1−ii−ii2i−2i0-1-111-1-111−i−iii−i−iii000000-11-11i−ii−i0i2−i2−22−i2i22−20000
χ27333333333333333333-1-10000000033-10000000000000000-1-1-1-1-1-100000000-111111111-1-1-1-1
χ28333333333333333333-1-10000000033-10000000000000000-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-11111
χ2933333333333333-3-3-3-3-1-100000000-3-3-10000000000000000-1-1-1-111000000001iiii−i−i−i−i−i−iii
χ3033333333333333-3-3-3-3-1-100000000-3-3-10000000000000000-1-1-1-111000000001−i−i−i−iiiiiii−i−i
χ313333-3-33333-3-3-3-33333-1-100000000-3-310000000000000000-1-111-1-100000000111-1-111-1-1-11-11
χ323333-3-33333-3-3-3-33333-1-100000000-3-310000000000000000-1-111-1-1000000001-1-111-1-1111-11-1
χ333333-3-33333-3-3-3-3-3-3-3-3-1-1000000003310000000000000000-1-1111100000000-1ii−i−i−i−iii−iii−i
χ343333-3-33333-3-3-3-3-3-3-3-3-1-1000000003310000000000000000-1-1111100000000-1−i−iiiii−i−ii−i−ii
χ35444444-1-1-1-1-1-1-1-100004444444444004-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ36444444-1-1-1-1-1-1-1-1000044-2-2-2-2-2-2-2-20041−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-1-1-1-100000000000000000000000
χ37444444-1-1-1-1-1-1-1-1000044-2-2-2-2-2-2-2-20041+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-1-1-1-100000000000000000000000
χ384444-4-4-1-1-1-111110000444444-4-4-4-400-4-1-1-1-1-1-1-1-111111111-1-11100000000000000000000000
χ394444-4-4-1-1-1-11111000044-2-2-2-2222200-41−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152-1-11100000000000000000000000
χ404444-4-4-1-1-1-11111000044-2-2-2-2222200-41+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152-1-11100000000000000000000000
χ4144-4-400-11-11−i5i5−i5i500004-44-44-40000000-1-1-1-11111−i5i5−i5i5i5−i5i5−i5-11−i5i500000000000000000000000
χ4244-4-400-11-11−i5i5−i5i500004-4-22-222323−23−230001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118-11−i5i500000000000000000000000
χ4344-4-400-11-11−i5i5−i5i500004-4-22-22−23−2323230001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94-11−i5i500000000000000000000000
χ4444-4-400-11-11i5−i5i5−i500004-44-44-40000000-1-1-1-11111i5−i5i5−i5−i5i5−i5i5-11i5−i500000000000000000000000
χ4544-4-400-11-11i5−i5i5−i500004-4-22-222323−23−230001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94-11i5−i500000000000000000000000
χ4644-4-400-11-11i5−i5i5−i500004-4-22-22−23−2323230001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118-11i5−i500000000000000000000000
χ474-44-44i−4i4-4-444i4i−4i−4i4-44-4001-1-11−ii−ii4i−4i011-1-111-1-1−i−iii−i−iii000000-11-11−ii−ii0000000000000
χ484-44-44i−4i4-4-444i4i−4i−4i-44-44001-1-11−ii−ii−4i4i011-1-111-1-1−i−iii−i−iii0000001-11-1i−ii−i0000000000000
χ494-44-4−4i4i4-4-44−4i−4i4i4i4-44-4001-1-11i−ii−i−4i4i011-1-111-1-1ii−i−iii−i−i000000-11-11i−ii−i0000000000000
χ504-44-4−4i4i4-4-44−4i−4i4i4i-44-44001-1-11i−ii−i4i−4i011-1-111-1-1ii−i−iii−i−i0000001-11-1−ii−ii0000000000000
χ514-4-440044-4-400004i−4i−4i4i0011-1-1−i3i3i3−i300011-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000−iii−i−333−30000000000000
χ524-4-440044-4-400004i−4i−4i4i0011-1-1i3−i3−i3i300011-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000−iii−i3−3−330000000000000
χ534-4-440044-4-400004i−4i−4i4i00-2-2220000000-2-22222-2-2000000000000002i−2i−2i2i00000000000000000
χ544-4-440044-4-40000−4i4i4i−4i0011-1-1−i3i3i3−i300011-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000i−i−ii3−3−330000000000000
χ554-4-440044-4-40000−4i4i4i−4i0011-1-1i3−i3−i3i300011-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000i−i−ii−333−30000000000000
χ564-4-440044-4-40000−4i4i4i−4i00-2-2220000000-2-22222-2-200000000000000−2i2i2i−2i00000000000000000
χ5766-6-6006-66-600006i6i−6i−6i-22000000000000000000000000000-2200−2i2i000000000000000000000
χ5866-6-6006-66-60000−6i−6i6i6i-22000000000000000000000000000-22002i−2i000000000000000000000
χ598-88-88i−8i-222-2−2i−2i2i2i0000002-2-22−2i2i−2i2i000−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118000000000000000000000000000
χ608-88-88i−8i-222-2−2i−2i2i2i0000002-2-22−2i2i−2i2i000−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94000000000000000000000000000
χ618-88-88i−8i-222-2−2i−2i2i2i000000-444-44i−4i4i−4i00011-1-111-1-1−i−iii−i−iii000000000000000000000000000
χ628-88-8−8i8i-222-22i2i−2i−2i0000002-2-222i−2i2i−2i000−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ118ζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118000000000000000000000000000
χ638-88-8−8i8i-222-22i2i−2i−2i0000002-2-222i−2i2i−2i000−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94000000000000000000000000000
χ648-88-8−8i8i-222-22i2i−2i−2i000000-444-4−4i4i−4i4i00011-1-111-1-1ii−i−iii−i−i000000000000000000000000000
χ658-8-8800-2-222−252525−2500000022-2-2−2i32i32i3−2i3000−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116000000000000000000000000000
χ668-8-8800-2-222−252525−2500000022-2-22i3−2i3−2i32i3000−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92000000000000000000000000000
χ678-8-8800-2-222−252525−25000000-4-444000000011-1-1-1-111−555−55−5−55000000000000000000000000000
χ688-8-8800-2-22225−25−252500000022-2-2−2i32i32i3−2i3000−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92000000000000000000000000000
χ698-8-8800-2-22225−25−252500000022-2-22i3−2i3−2i32i3000−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116000000000000000000000000000
χ708-8-8800-2-22225−25−2525000000-4-444000000011-1-1-1-1115−5−55−555−5000000000000000000000000000
χ71121212121212-3-3-3-3-3-3-3-30000-4-40000000000-40000000000000000111100000000000000000000000
χ7212121212-12-12-3-3-3-333330000-4-400000000004000000000000000011-1-100000000000000000000000
χ731212-12-1200-33-33−3i53i5−3i53i50000-440000000000000000000000000001-1i5−i500000000000000000000000
χ741212-12-1200-33-333i5−3i53i5−3i50000-440000000000000000000000000001-1−i5i500000000000000000000000

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