Finite Group Databasebeta

← Group #11721105

Character table — Group #11721105

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111111112222222266666666666666661212121212121212181818181818181818181818181818181818181818181818181818181818181818181818
order1222444436661212121233666666121212121212121236661212121222444444444466661212121212121212121212121212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ71111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ81111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911-1-111-1-111-1-111-1-111-1-11-1-1111-1-111-1-11-1-1111-1-11-11-1i−ii−ii−ii−i11-1-1ii−i−iii−i−iii−i−iii−i−i11-1-1
χ1011-1-111-1-111-1-111-1-111-1-11-1-1111-1-111-1-11-1-1111-1-11-11-1−ii−ii−ii−ii11-1-1−i−iii−i−iii−i−iii−i−iii11-1-1
χ1111-1-111-1-111-1-111-1-111-1-11-1-1111-1-111-1-11-1-1111-1-1-11-11i−ii−i−ii−ii-1-111ii−i−iii−i−i−i−iii−i−iii-1-111
χ1211-1-111-1-111-1-111-1-111-1-11-1-1111-1-111-1-11-1-1111-1-1-11-11−ii−iii−ii−i-1-111−i−iii−i−iiiii−i−iii−i−i-1-111
χ1311-1-1-1-11111-1-1-1-11111-1-11-1-11-1-111-1-1111-1-11-1-1111-1-11i−i−iii−i−ii11-1-1ii−i−i−i−iiiii−i−i−i−iii-1-111
χ1411-1-1-1-11111-1-1-1-11111-1-11-1-11-1-111-1-1111-1-11-1-1111-1-11−iii−i−iii−i11-1-1−i−iiiii−i−i−i−iiiii−i−i-1-111
χ1511-1-1-1-11111-1-1-1-11111-1-11-1-11-1-111-1-1111-1-11-1-111-111-1i−i−ii−iii−i-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-1
χ1611-1-1-1-11111-1-1-1-11111-1-11-1-11-1-111-1-1111-1-11-1-111-111-1−iii−ii−i−ii-1-111−i−iiiii−i−iii−i−i−i−iii11-1-1
χ1722222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-10000000000000000-1-1-1-1
χ1822222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000111100000000000000001111
χ192222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1000000002222000000000000-1-1-1-1-1-1-1-10000
χ202222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000111111110000
χ212222-2-2-2-22222-2-2-2-22-1-1-1222-1-2-2-2-21111-1-1-1-1111122-2-200000000-1-1-1-100000000000000001111
χ222222-2-2-2-22222-2-2-2-22-1-1-1222-1-2-2-2-21111-1-1-1-11111-2-2220000000011110000000000000000-1-1-1-1
χ232222-2-2-2-22222-2-2-2-2-1222-1-1-121111-2-2-2-2-1-1-1-111110000000022-2-2000000000000-1-1-1-111110000
χ242222-2-2-2-22222-2-2-2-2-1222-1-1-121111-2-2-2-2-1-1-1-1111100000000-2-2220000000000001111-1-1-1-10000
χ2522-2-222-2-222-2-222-2-22-1112-2-2-122-2-2-1-111-111-1-1-1112-22-200000000-1-1110000000000000000-1-111
χ2622-2-222-2-222-2-222-2-22-1112-2-2-122-2-2-1-111-111-1-1-111-22-220000000011-1-1000000000000000011-1-1
χ2722-2-222-2-222-2-222-2-2-12-2-2-1112-1-11122-2-2-111-1-1-111000000002i−2i2i−2i000000000000−i−iii−i−iii0000
χ2822-2-222-2-222-2-222-2-2-12-2-2-1112-1-11122-2-2-111-1-1-11100000000−2i2i−2i2i000000000000ii−i−iii−i−i0000
χ2922-2-2-2-22222-2-2-2-2222-1112-2-2-1-2-22211-1-1-111-111-1-12-2-2200000000-1-111000000000000000011-1-1
χ3022-2-2-2-22222-2-2-2-2222-1112-2-2-1-2-22211-1-1-111-111-1-1-222-20000000011-1-10000000000000000-1-111
χ3122-2-2-2-22222-2-2-2-222-12-2-2-111211-1-1-2-222-111-111-1-1000000002i−2i−2i2i000000000000−i−iiiii−i−i0000
χ3222-2-2-2-22222-2-2-2-222-12-2-2-111211-1-1-2-222-111-111-1-100000000−2i2i2i−2i000000000000ii−i−i−i−iii0000
χ332-22-22i−2i2i−2i2-22-22i−2i2i−2i222-2-22-2-22i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000000000000000000000
χ342-22-22i−2i2i−2i2-22-22i−2i2i−2i2-1-11-22-212i−2i2i−2i−ii−ii-1-111−ii−ii000000000000−i3i3−i3i300000000000000003−33−3
χ352-22-22i−2i2i−2i2-22-22i−2i2i−2i2-1-11-22-212i−2i2i−2i−ii−ii-1-111−ii−ii000000000000i3−i3i3−i30000000000000000−33−33
χ362-22-22i−2i2i−2i2-22-22i−2i2i−2i-122-21-11-2−ii−ii2i−2i2i−2i-1-111−ii−ii0000000000000000000000003−33−3−i3i3−i3i30000
χ372-22-22i−2i2i−2i2-22-22i−2i2i−2i-122-21-11-2−ii−ii2i−2i2i−2i-1-111−ii−ii000000000000000000000000−33−33i3−i3i3−i30000
χ382-22-2−2i2i−2i2i2-22-2−2i2i−2i2i222-2-22-2-2−2i2i−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i000000000000000000000000000000000000
χ392-22-2−2i2i−2i2i2-22-2−2i2i−2i2i2-1-11-22-21−2i2i−2i2ii−ii−i-1-111i−ii−i000000000000−i3i3−i3i30000000000000000−33−33
χ402-22-2−2i2i−2i2i2-22-2−2i2i−2i2i2-1-11-22-21−2i2i−2i2ii−ii−i-1-111i−ii−i000000000000i3−i3i3−i300000000000000003−33−3
χ412-22-2−2i2i−2i2i2-22-2−2i2i−2i2i-122-21-11-2i−ii−i−2i2i−2i2i-1-111i−ii−i0000000000000000000000003−33−3i3−i3i3−i30000
χ422-22-2−2i2i−2i2i2-22-2−2i2i−2i2i-122-21-11-2i−ii−i−2i2i−2i2i-1-111i−ii−i000000000000000000000000−33−33−i3i3−i3i30000
χ432-2-222i−2i−2i2i2-2-222i−2i−2i2i22-22-2-22-22i−2i−2i2i2i−2i−2i2i2-22-22i−2i−2i2i000000000000000000000000000000000000
χ442-2-222i−2i−2i2i2-2-222i−2i−2i2i2-11-1-2-2212i−2i−2i2i−iii−i-11-11−iii−i000000000000−i3i3i3−i300000000000000003−3−33
χ452-2-222i−2i−2i2i2-2-222i−2i−2i2i2-11-1-2-2212i−2i−2i2i−iii−i-11-11−iii−i000000000000i3−i3−i3i30000000000000000−333−3
χ462-2-222i−2i−2i2i2-2-222i−2i−2i2i-12-2211-1-2−iii−i2i−2i−2i2i-11-11−iii−i000000000000000000000000−i3i3i3−i3−333−30000
χ472-2-222i−2i−2i2i2-2-222i−2i−2i2i-12-2211-1-2−iii−i2i−2i−2i2i-11-11−iii−i000000000000000000000000i3−i3−i3i33−3−330000
χ482-2-22−2i2i2i−2i2-2-22−2i2i2i−2i22-22-2-22-2−2i2i2i−2i−2i2i2i−2i2-22-2−2i2i2i−2i000000000000000000000000000000000000
χ492-2-22−2i2i2i−2i2-2-22−2i2i2i−2i2-11-1-2-221−2i2i2i−2ii−i−ii-11-11i−i−ii000000000000−i3i3i3−i30000000000000000−333−3
χ502-2-22−2i2i2i−2i2-2-22−2i2i2i−2i2-11-1-2-221−2i2i2i−2ii−i−ii-11-11i−i−ii000000000000i3−i3−i3i300000000000000003−3−33
χ512-2-22−2i2i2i−2i2-2-22−2i2i2i−2i-12-2211-1-2i−i−ii−2i2i2i−2i-11-11i−i−ii000000000000000000000000−i3i3i3−i33−3−330000
χ522-2-22−2i2i2i−2i2-2-22−2i2i2i−2i-12-2211-1-2i−i−ii−2i2i2i−2i-11-11i−i−ii000000000000000000000000i3−i3−i3i3−333−30000
χ534444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000
χ544444-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-2-2222222221111-1-1-1-1000000000000000000000000000000000000
χ5544-4-444-4-444-4-444-4-4-2-222-222-2-2-222-2-2221-1-1111-1-1000000000000000000000000000000000000
χ5644-4-4-4-44444-4-4-4-444-2-222-222-222-2-222-2-21-1-11-1-111000000000000000000000000000000000000
χ574-44-44i−4i4i−4i4-44-44i−4i4i−4i-2-2-222-222−2i2i−2i2i−2i2i−2i2i11-1-1i−ii−i000000000000000000000000000000000000
χ584-44-4−4i4i−4i4i4-44-4−4i4i−4i4i-2-2-222-2222i−2i2i−2i2i−2i2i−2i11-1-1−ii−ii000000000000000000000000000000000000
χ594-4-444i−4i−4i4i4-4-444i−4i−4i4i-2-22-222-22−2i2i2i−2i−2i2i2i−2i1-11-1i−i−ii000000000000000000000000000000000000
χ604-4-44−4i4i4i−4i4-4-44−4i4i4i−4i-2-22-222-222i−2i−2i2i2i−2i−2i2i1-11-1−iii−i000000000000000000000000000000000000
χ6166666666-3-3-3-3-3-3-3-30000000000000000000000000000222200000000-1-1-1-1-1-1-1-1000000000000
χ6266666666-3-3-3-3-3-3-3-30000000000000000000000000000-2-2-2-20000000011111111000000000000
χ636666-6-6-6-6-3-3-3-33333000000000000000000000000000022-2-200000000-1-1-1-11111000000000000
χ646666-6-6-6-6-3-3-3-333330000000000000000000000000000-2-222000000001111-1-1-1-1000000000000
χ6566-6-666-6-6-3-333-3-33300000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii000000000000
χ6666-6-666-6-6-3-333-3-3330000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i000000000000
χ6766-6-6-6-666-3-33333-3-300000000000000000000000000002i−2i−2i2i00000000−i−iiiii−i−i000000000000
χ6866-6-6-6-666-3-33333-3-30000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii000000000000
χ696-66-66i−6i6i−6i-33-33−3i3i−3i3i0000000000000000000000000000000000000000−i3i3−i3i33−33−3000000000000
χ706-66-66i−6i6i−6i-33-33−3i3i−3i3i0000000000000000000000000000000000000000i3−i3i3−i3−33−33000000000000
χ716-66-6−6i6i−6i6i-33-333i−3i3i−3i0000000000000000000000000000000000000000−i3i3−i3i3−33−33000000000000
χ726-66-6−6i6i−6i6i-33-333i−3i3i−3i0000000000000000000000000000000000000000i3−i3i3−i33−33−3000000000000
χ736-6-666i−6i−6i6i-333-3−3i3i3i−3i00000000000000000000000000000000000000003−3−33i3−i3−i3i3000000000000
χ746-6-666i−6i−6i6i-333-3−3i3i3i−3i0000000000000000000000000000000000000000−333−3−i3i3i3−i3000000000000
χ756-6-66−6i6i6i−6i-333-33i−3i−3i3i00000000000000000000000000000000000000003−3−33−i3i3i3−i3000000000000
χ766-6-66−6i6i6i−6i-333-33i−3i−3i3i0000000000000000000000000000000000000000−333−3i3−i3−i3i3000000000000

Here i is the imaginary unit (i² = −1).