Finite Group Databasebeta

← Group #70906

Character table — Group #70906

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111112222222222224444444444444444888888888888121212121212121224242424
order122244443444466612121212888812121212242424242424242444441212121212121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ101111-1-1-1-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−ii−ii
χ111111-1-1-1-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−ii−ii
χ121111-1-1-1-1111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiii−ii−i
χ131111-1-1-1-1111-1-1111-1-1-1-1-1-111-1-111-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ141111-1-1-1-1111-1-1111-1-1-1-1-1-111-1-111-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ151111-1-1-1-1111-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ161111-1-1-1-1111-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222-2-2-2-222222220000-2-2-2-2000000000000000000002-22-200000000
χ18222222222-2-2-2-222222220000-2-2-2-200000000000000000000-22-2200000000
χ1922222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ232222-2-2-2-22-2-222222-2-2-2-2000022-2-2000000000000000000002i−2i−2i2i00000000
χ242222-2-2-2-22-2-222222-2-2-2-2000022-2-200000000000000000000−2i2i2i−2i00000000
χ252222-2-2-2-2-122-2-2-1-1-1111122-2-211-1-1-1-1-1-111112-22-2-1-111-1-111000000000000
χ262222-2-2-2-2-122-2-2-1-1-1111122-2-211-1-1-1-1-1-11111-22-2211-1-111-1-1000000000000
χ272222-2-2-2-2-122-2-2-1-1-11111-2-22211-1-11111-1-1-1-12-2-22-1-11111-1-1000000000000
χ282222-2-2-2-2-122-2-2-1-1-11111-2-22211-1-11111-1-1-1-1-222-211-1-1-1-111000000000000
χ292-22-22i2i−2i−2i22-22i−2i-22-22i2i−2i−2i00002i−2i2-20000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ302-22-22i2i−2i−2i22-22i−2i-22-22i2i−2i−2i00002i−2i2-2000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ312-22-22i2i−2i−2i2-22−2i2i-22-22i2i−2i−2i2i−2i2-2−2i2i-222i2i−2i−2i22-2-2000000000000000000000000
χ322-22-22i2i−2i−2i2-22−2i2i-22-22i2i−2i−2i−2i2i-22−2i2i-22−2i−2i2i2i-2-222000000000000000000000000
χ332-22-22i2i−2i−2i-1-22−2i2i1-11−i−iii2i−2i2-2i−i1-1−i−iii-1-1110000−i3i33−33−3−i3i3000000000000
χ342-22-22i2i−2i−2i-1-22−2i2i1-11−i−iii2i−2i2-2i−i1-1−i−iii-1-1110000i3−i3−33−33i3−i3000000000000
χ352-22-22i2i−2i−2i-1-22−2i2i1-11−i−iii−2i2i-22i−i1-1ii−i−i11-1-10000−i3i33−3−33i3−i3000000000000
χ362-22-22i2i−2i−2i-1-22−2i2i1-11−i−iii−2i2i-22i−i1-1ii−i−i11-1-10000i3−i3−333−3−i3i3000000000000
χ372-22-2−2i−2i2i2i22-2−2i2i-22-2−2i−2i2i2i0000−2i2i2-2000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ382-22-2−2i−2i2i2i22-2−2i2i-22-2−2i−2i2i2i0000−2i2i2-20000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ392-22-2−2i−2i2i2i2-222i−2i-22-2−2i−2i2i2i2i−2i-222i−2i-222i2i−2i−2i-2-222000000000000000000000000
χ402-22-2−2i−2i2i2i2-222i−2i-22-2−2i−2i2i2i−2i2i2-22i−2i-22−2i−2i2i2i22-2-2000000000000000000000000
χ412-22-2−2i−2i2i2i-1-222i−2i1-11ii−i−i2i−2i-22−ii1-1−i−iii11-1-10000−i3i3−333−3i3−i3000000000000
χ422-22-2−2i−2i2i2i-1-222i−2i1-11ii−i−i2i−2i-22−ii1-1−i−iii11-1-10000i3−i33−3−33−i3i3000000000000
χ432-22-2−2i−2i2i2i-1-222i−2i1-11ii−i−i−2i2i2-2−ii1-1ii−i−i-1-1110000−i3i3−33−33−i3i3000000000000
χ442-22-2−2i−2i2i2i-1-222i−2i1-11ii−i−i−2i2i2-2−ii1-1ii−i−i-1-1110000i3−i33−33−3i3−i3000000000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ464444-4-4-4-4-2-4-444-2-2-222220000-2-22200000000000000000000000000000000
χ4744-4-44-44-4400004-4-44-44-40000000000000000000000000000000000000000
χ4844-4-44-44-4-20000-222-22-2200000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ4944-4-44-44-4-20000-222-22-2200000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ5044-4-4-44-44400004-4-4-44-440000000000000000000000000000000000000000
χ5144-4-4-44-44-20000-2222-22-200000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ5244-4-4-44-44-20000-2222-22-200000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ534-44-44i4i−4i−4i-24-44i−4i2-22−2i−2i2i2i0000−2i2i-2200000000000000000000000000000000
χ544-44-4−4i−4i4i4i-24-4−4i4i2-222i2i−2i−2i00002i−2i-2200000000000000000000000000000000
χ554-4-444i−4i−4i4i40000-4-444i−4i−4i4i0000000000000000000000000000000000000000
χ564-4-444i−4i−4i4i-2000022-2−2i2i2i−2i000000006−6−66−i6i6i6−i6000000000000000000000000
χ574-4-444i−4i−4i4i-2000022-2−2i2i2i−2i00000000−666−6i6−i6−i6i6000000000000000000000000
χ584-4-44−4i4i4i−4i40000-4-44−4i4i4i−4i0000000000000000000000000000000000000000
χ594-4-44−4i4i4i−4i-2000022-22i−2i−2i2i000000006−6−66i6−i6−i6i6000000000000000000000000
χ604-4-44−4i4i4i−4i-2000022-22i−2i−2i2i00000000−666−6−i6i6i6−i6000000000000000000000000

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