Finite Group Databasebeta

← Group #11721109

Character table — Group #11721109

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11112222224466666666666612121212121212121212181818181818181818181818363636363636363636363636
order122234466612123366666612121212366612121212121244441212121212121212244466121212121212
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1
χ511111-1-1111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ611111-1-1111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111
χ711111-1-1111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-111111-1-1-1-1
χ811111-1-1111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-1-11111
χ92222222222222-1-12-122-12222-1-1-1-1-1-1-1-1-1-10000000000002020-1-10000-1-1
χ102222222222222-1-12-122-12222-1-1-1-1-1-1-1-1-1-1000000000000-20-2011000011
χ11222222222222-122-12-1-12-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ12222222222222-122-12-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111000000000000
χ1322222-2-2222-2-22-1-12-122-1-2-2-2-2-1-1-1-111111100000000000020-20-1-1000011
χ1422222-2-2222-2-22-1-12-122-1-2-2-2-2-1-1-1-1111111000000000000-2020110000-1-1
χ1522222-2-2222-2-2-122-12-1-121111-1-1-1-1-2-2111122-2-2-1-1-1-11111000000000000
χ1622222-2-2222-2-2-122-12-1-121111-1-1-1-1-2-21111-2-2221111-1-1-1-1000000000000
χ1722-2-2200-2-220022-222-2-2-200002-2-22000000002i−2i00002i2i−2i−2i000000000000
χ1822-2-2200-2-220022-222-2-2-200002-2-2200000000−2i2i0000−2i−2i2i2i000000000000
χ1922-2-2200-2-2200-12-2-1211-2−i3−i3i3i3-111-100−i3−i3i3i3002i−2i33−3−3−i−iii000000000000
χ2022-2-2200-2-2200-12-2-1211-2−i3−i3i3i3-111-100−i3−i3i3i300−2i2i−3−333ii−i−i000000000000
χ2122-2-2200-2-2200-12-2-1211-2i3i3−i3−i3-111-100i3i3−i3−i3002i−2i−3−333−i−iii000000000000
χ2222-2-2200-2-2200-12-2-1211-2i3i3−i3−i3-111-100i3i3−i3−i300−2i2i33−3−3ii−i−i000000000000
χ232-22-22002-2-20022-2-2-22-22000022-2-20000002i−2i002i−2i2i−2i0000000000000000
χ242-22-22002-2-20022-2-2-22-22000022-2-2000000−2i2i00−2i2i−2i2i0000000000000000
χ252-22-22002-2-200-12-21-2-1123−33−3-1-111003−33−32i−2i00−ii−ii−i3i3−i3i3000000000000
χ262-22-22002-2-200-12-21-2-1123−33−3-1-111003−33−3−2i2i00i−ii−ii3−i3i3−i3000000000000
χ272-22-22002-2-200-12-21-2-112−33−33-1-11100−33−332i−2i00−ii−iii3−i3i3−i3000000000000
χ282-22-22002-2-200-12-21-2-112−33−33-1-11100−33−33−2i2i00i−ii−i−i3i3−i3i3000000000000
χ292-2-2222i−2i-22-22i−2i222-2-2-22-22i−2i−2i2i2-22-22i−2i2i−2i−2i2i000000000000000000000000
χ302-2-2222i−2i-22-22i−2i2-1-1-21-2212i−2i−2i2i-11-11−ii−iii−i0000000000000000−i3i300003−3
χ312-2-2222i−2i-22-22i−2i2-1-1-21-2212i−2i−2i2i-11-11−ii−iii−i0000000000000000i3−i30000−33
χ322-2-2222i−2i-22-22i−2i-1221-21-1-2−iii−i-11-112i−2i−iii−i0000−i3i3i3−i3−333−3000000000000
χ332-2-2222i−2i-22-22i−2i-1221-21-1-2−iii−i-11-112i−2i−iii−i0000i3−i3−i3i33−3−33000000000000
χ342-2-222−2i2i-22-2−2i2i222-2-2-22-2−2i2i2i−2i2-22-2−2i2i−2i2i2i−2i000000000000000000000000
χ352-2-222−2i2i-22-2−2i2i2-1-1-21-221−2i2i2i−2i-11-11i−ii−i−ii0000000000000000−i3i30000−33
χ362-2-222−2i2i-22-2−2i2i2-1-1-21-221−2i2i2i−2i-11-11i−ii−i−ii0000000000000000i3−i300003−3
χ372-2-222−2i2i-22-2−2i2i-1221-21-1-2i−i−ii-11-11−2i2ii−i−ii0000−i3i3i3−i33−3−33000000000000
χ382-2-222−2i2i-22-2−2i2i-1221-21-1-2i−i−ii-11-11−2i2ii−i−ii0000i3−i3−i3i3−333−3000000000000
χ39444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-21111000000000000000000000000
χ4044444-4-4444-4-4-2-2-2-2-2-2-2-22222111122-1-1-1-1000000000000000000000000
χ4144-4-4400-4-44004-224-2-4-420000-222-2000000000000000000000000000000
χ4244-4-4400-4-4400-2-22-2-2222−2i3−2i32i32i31-1-1100i3i3−i3−i3000000000000000000000000
χ4344-4-4400-4-4400-2-22-2-22222i32i3−2i3−2i31-1-1100−i3−i3i3i3000000000000000000000000
χ444-44-44004-4-4004-22-424-4-20000-2-222000000000000000000000000000000
χ454-44-44004-4-400-2-2222-22-223−2323−2311-1-100−33−33000000000000000000000000
χ464-44-44004-4-400-2-2222-22-2−2323−232311-1-1003−33−3000000000000000000000000
χ474-4-4444i−4i-44-44i−4i-2-2-2222-22−2i2i2i−2i1-11-1−2i2ii−i−ii000000000000000000000000
χ484-4-444−4i4i-44-4−4i4i-2-2-2222-222i−2i−2i2i1-11-12i−2i−iii−i000000000000000000000000
χ496666-366-3-3-3-3-30000000000000000000000000000000000020200-1-1-1-100
χ506666-366-3-3-3-3-300000000000000000000000000000000000-20-200111100
χ516666-3-6-6-3-3-3330000000000000000000000000000000000020-20011-1-100
χ526666-3-6-6-3-3-33300000000000000000000000000000000000-20200-1-11100
χ536-6-66-36i−6i3-33−3i3i0000000000000000000000000000000000000000−i3i33−300
χ546-6-66-36i−6i3-33−3i3i0000000000000000000000000000000000000000i3−i3−3300
χ556-6-66-3−6i6i3-333i−3i0000000000000000000000000000000000000000−i3i3−3300
χ566-6-66-3−6i6i3-333i−3i0000000000000000000000000000000000000000i3−i33−300
χ571212-12-12-60066-6000000000000000000000000000000000000000000000000
χ5812-1212-12-600-666000000000000000000000000000000000000000000000000

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