Finite Group Databasebeta

← Group #11777700

Character table — Group #11777700

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888881212121212121212181818181818181824242424242424242424242424242424242424243636363636363636
order12224444336666668812121212121212122424242424242424444488884444888844881212121212121212242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i11-1-111-1-1ii−i−iii−i−i11-1-1ii−i−i
χ101111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i-11−ii11-1-1-1-111−i−iiiii−i−i-1-111−i−iii
χ111111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-111−i−iii11-1-1ii−i−i1-1i−i-1-11111-1-1ii−i−i−i−iii-1-111−i−iii
χ121111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-111−i−iii11-1-1ii−i−i-11−ii-1-111-1-111−i−iii−i−iii11-1-1ii−i−i
χ131111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii11-1-111-1-1−i−iii−i−iii11-1-1−i−iii
χ141111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii-11i−i11-1-1-1-111ii−i−i−i−iii-1-111ii−i−i
χ151111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii-1-111ii−i−i11-1-1−i−iii1-1−ii-1-11111-1-1−i−iiiii−i−i-1-111ii−i−i
χ161111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−iii-1-111ii−i−i11-1-1−i−iii-11i−i-1-111-1-111ii−i−iii−i−i11-1-1−i−iii
χ17222222222222222222222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-222222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000
χ192222-2-2-2-2222222222i−2i-2-2-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i00000000-2-222−2i−2i2i2i0000000000000000000000000000
χ202222-2-2-2-222222222−2i2i-2-2-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i00000000-2-2222i2i−2i−2i0000000000000000000000000000
χ212-22-22i−2i2i−2i22-2-222-2-2002i−2i2i−2i2i−2i2i−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000002−2−i2i21−i−1+i1+i−1−i
χ222-22-22i−2i2i−2i22-2-222-2-2002i−2i2i−2i2i−2i2i−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000−22i2−i2−1+i1−i−1−i1+i
χ232-22-22i−2i2i−2i22-2-222-2-2002i−2i2i−2i2i−2i2i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000002−2−i2i2−1+i1−i−1−i1+i
χ242-22-22i−2i2i−2i22-2-222-2-2002i−2i2i−2i2i−2i2i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−22i2−i21−i−1+i1+i−1−i
χ252-22-2−2i2i−2i2i22-2-222-2-200−2i2i−2i2i−2i2i−2i2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000002−2i2−i21+i−1−i1−i−1+i
χ262-22-2−2i2i−2i2i22-2-222-2-200−2i2i−2i2i−2i2i−2i2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−22−i2i2−1−i1+i−1+i1−i
χ272-22-2−2i2i−2i2i22-2-222-2-200−2i2i−2i2i−2i2i−2i2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000002−2i2−i2−1−i1+i−1+i1−i
χ282-22-2−2i2i−2i2i22-2-222-2-200−2i2i−2i2i−2i2i−2i2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000−22−i2i21+i−1−i1−i−1+i
χ292-2-222i−2i−2i2i22-2-2-2-22200−2i2i2i−2i−2i2i2i−2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-22i−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ302-2-222i−2i−2i2i22-2-2-2-22200−2i2i2i−2i−2i2i2i−2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-22i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ312-2-222i−2i−2i2i22-2-2-2-22200−2i2i2i−2i−2i2i2i−2i000000002i−2i2-20000-22−2i2i000000002i−2i2-200000000000000000000
χ322-2-222i−2i−2i2i22-2-2-2-22200−2i2i2i−2i−2i2i2i−2i00000000−2i2i-220000-22−2i2i00000000−2i2i-2200000000000000000000
χ332-2-22−2i2i2i−2i22-2-2-2-222002i−2i−2i2i2i−2i−2i2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-2−2i2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ342-2-22−2i2i2i−2i22-2-2-2-222002i−2i−2i2i2i−2i−2i2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-2−2i2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ352-2-22−2i2i2i−2i22-2-2-2-222002i−2i−2i2i2i−2i−2i2i000000002i−2i-220000-222i−2i000000002i−2i-2200000000000000000000
χ362-2-22−2i2i2i−2i22-2-2-2-222002i−2i−2i2i2i−2i−2i2i00000000−2i2i2-20000-222i−2i00000000−2i2i2-200000000000000000000
χ37444444441-21-21-21-24411-2-2-2-211-2-2-2-2111122222222000000000000-1-1-1-100000000-1-1-1-100000000
χ38444444441-21-21-21-24411-2-2-2-211-2-2-2-21111-2-2-2-2-2-2-2-2000000000000111100000000111100000000
χ39444444441-21-21-21-2-4-411-2-2-2-2112222-1-1-1-12222-2-2-2-2000000000000-1-1-1-100000000111100000000
χ40444444441-21-21-21-2-4-411-2-2-2-2112222-1-1-1-1-2-2-2-22222000000000000111100000000-1-1-1-100000000
χ4144444444-21-21-21-2144-2-21111-2-21111-2-2-2-2000000000000000022220000-1-1-1-1-1-1-1-1000000000000
χ4244444444-21-21-21-2144-2-21111-2-21111-2-2-2-20000000000000000-2-2-2-2000011111111000000000000
χ4344444444-21-21-21-21-4-4-2-21111-2-2-1-1-1-12222000000000000000022-2-20000-1-1-1-11111000000000000
χ4444444444-21-21-21-21-4-4-2-21111-2-2-1-1-1-122220000000000000000-2-22200001111-1-1-1-1000000000000
χ454444-4-4-4-41-21-21-21-24i−4i-1-12222-1-1−2i−2i2i2iii−i−i22-2-22i2i−2i−2i000000000000-1-11100000000−i−iii00000000
χ464444-4-4-4-41-21-21-21-24i−4i-1-12222-1-1−2i−2i2i2iii−i−i-2-222−2i−2i2i2i00000000000011-1-100000000ii−i−i00000000
χ474444-4-4-4-41-21-21-21-2−4i4i-1-12222-1-12i2i−2i−2i−i−iii22-2-2−2i−2i2i2i000000000000-1-11100000000ii−i−i00000000
χ484444-4-4-4-41-21-21-21-2−4i4i-1-12222-1-12i2i−2i−2i−i−iii-2-2222i2i−2i−2i00000000000011-1-100000000−i−iii00000000
χ494444-4-4-4-4-21-21-21-214i−4i22-1-1-1-122ii−i−i−2i−2i2i2i00000000000000002-22i−2i0000-1-111−i−iii000000000000
χ504444-4-4-4-4-21-21-21-214i−4i22-1-1-1-122ii−i−i−2i−2i2i2i0000000000000000-22−2i2i000011-1-1ii−i−i000000000000
χ514444-4-4-4-4-21-21-21-21−4i4i22-1-1-1-122−i−iii2i2i−2i−2i00000000000000002-2−2i2i0000-1-111ii−i−i000000000000
χ524444-4-4-4-4-21-21-21-21−4i4i22-1-1-1-122−i−iii2i2i−2i−2i0000000000000000-222i−2i000011-1-1−i−iii000000000000
χ5344-4-444-4-44444-4-4-4-400-4-444-4-4440000000000000000000000000000000000000000000000000000
χ5444-4-444-4-4-21-212-12-1002211-1-1-2-23-33-300000000000000000000000000003−33−33−33−3000000000000
χ5544-4-444-4-4-21-212-12-1002211-1-1-2-23-33-30000000000000000000000000000−33−33−33−33000000000000
χ5644-4-444-4-4-21-212-12-1002211-1-1-2-2-33-3300000000000000000000000000003−33−3−33−33000000000000
χ5744-4-444-4-4-21-212-12-1002211-1-1-2-2-33-330000000000000000000000000000−33−333−33−3000000000000
χ5844-4-4-4-4444444-4-4-4-40044-4-444-4-40000000000000000000000000000000000000000000000000000
χ5944-4-4-4-444-21-212-12-100-2-2-1-111223i−3i−3i3i00000000000000000000000000003−3−33i3−i3−i3i3000000000000
χ6044-4-4-4-444-21-212-12-100-2-2-1-111223i−3i−3i3i0000000000000000000000000000−333−3−i3i3i3−i3000000000000
χ6144-4-4-4-444-21-212-12-100-2-2-1-11122−3i3i3i−3i00000000000000000000000000003−3−33−i3i3i3−i3000000000000
χ6244-4-4-4-444-21-212-12-100-2-2-1-11122−3i3i3i−3i0000000000000000000000000000−333−3i3−i3−i3i3000000000000
χ634-4-444i−4i−4i4i1-2-12-121-200−ii−2i2i2i−2ii−i00003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ132i−2i2-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−ii-1100000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2300000000
χ644-4-444i−4i−4i4i1-2-12-121-200−ii−2i2i2i−2ii−i00003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ13−2i2i-222ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000i−i1-100000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2300000000
χ654-4-444i−4i−4i4i1-2-12-121-200−ii−2i2i2i−2ii−i0000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ132i−2i2-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−ii-1100000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2300000000
χ664-4-444i−4i−4i4i1-2-12-121-200−ii−2i2i2i−2ii−i0000−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ13−2i2i-22−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000i−i1-100000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2300000000
χ674-4-44−4i4i4i−4i1-2-12-121-200i−i2i−2i−2i2i−ii0000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ232i−2i-22−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−ii1-100000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300000000
χ684-4-44−4i4i4i−4i1-2-12-121-200i−i2i−2i−2i2i−ii0000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ23−2i2i2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000i−i-1100000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300000000
χ694-4-44−4i4i4i−4i1-2-12-121-200i−i2i−2i−2i2i−ii00003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ232i−2i-222ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ii1-100000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300000000
χ704-4-44−4i4i4i−4i1-2-12-121-200i−i2i−2i−2i2i−ii00003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23−2i2i2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000i−i-1100000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300000000
χ7188-8-888-8-82-42-4-24-2400-2-2-4-444220000000000000000000000000000000000000000000000000000
χ7288-8-8-8-8882-42-4-24-24002244-4-4-2-20000000000000000000000000000000000000000000000000000
χ738-88-88i−8i8i−8i2-4-242-4-24002i−2i−4i4i−4i4i2i−2i0000000000000000000000000000000000000000000000000000
χ748-88-88i−8i8i−8i-424-2-424-200−4i4i2i−2i2i−2i−4i4i0000000000000000000000000000000000000000000000000000
χ758-88-8−8i8i−8i8i2-4-242-4-2400−2i2i4i−4i4i−4i−2i2i0000000000000000000000000000000000000000000000000000
χ768-88-8−8i8i−8i8i-424-2-424-2004i−4i−2i2i−2i2i4i−4i0000000000000000000000000000000000000000000000000000
χ778-8-888i−8i−8i8i-424-24-2-42004i−4i2i−2i−2i2i−4i4i0000000000000000000000000000000000000000000000000000
χ788-8-88−8i8i8i−8i-424-24-2-4200−4i4i−2i2i2i−2i4i−4i0000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.