Finite Group Databasebeta

← Group #13180661

Character table — Group #13180661

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112334444444468888991212121212121212161616161616161616161616161616161827275472727272108108108108108108108108
order1222233666666236664466666666333366666666666644441212121288888888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511-1111111-1-1-1-1-11-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-11-11-11-11-1
χ611-1111111-1-1-1-1-11-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-11-11-11-11
χ711-1111111-1-1-1-1-11-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111i−i−iii−i−ii
χ811-1111111-1-1-1-1-11-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111−iii−i−iii−i
χ922222222222222-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100000000
χ1022222222222222-1-1-1-1-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100000000
χ1122-2222222-2-2-2-2-2-111-1222222-2-2-2-2-1-1-1-1-1-1-1-111111111-222-2-1-11100000000
χ1222-2222222-2-2-2-2-2-111-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111112-2-2211-1-100000000
χ132-202-222-2-200000200-22i−2i22-2-200002222-2-2-2-20000000002i−2i02i−2i0000000000
χ142-202-222-2-200000200-2−2i2i22-2-200002222-2-2-2-2000000000−2i2i0−2i2i0000000000
χ152-202-222-2-200000-1−i3i312i−2i22-2-20000-1-1-1-11111−i3−i3−i3−i3i3i3i3i302i−2i0−ii3−300000000
χ162-202-222-2-200000-1−i3i31−2i2i22-2-20000-1-1-1-11111−i3−i3−i3−i3i3i3i3i30−2i2i0i−i−3300000000
χ172-202-222-2-200000-1i3−i312i−2i22-2-20000-1-1-1-11111i3i3i3i3−i3−i3−i3−i302i−2i0−ii−3300000000
χ182-202-222-2-200000-1i3−i31−2i2i22-2-20000-1-1-1-11111i3i3i3i3−i3−i3−i3−i30−2i2i0i−i3−300000000
χ19333-1-133333333-1000033-1-1-1-1-1-1-1-100000000000000003-1-1-100001111-1-1-1-1
χ20333-1-133333333-1000033-1-1-1-1-1-1-1-100000000000000003-1-1-10000-1-1-1-11111
χ21333-1-133333333-10000-3-3-1-1-1-1-1-1-1-10000000000000000-31110000ii−i−i−i−iii
χ22333-1-133333333-10000-3-3-1-1-1-1-1-1-1-10000000000000000-31110000−i−iiiii−i−i
χ2333-3-1-13333-3-3-3-31000033-1-1-1-111110000000000000000-3-1-1100001-11-1-11-11
χ2433-3-1-13333-3-3-3-31000033-1-1-1-111110000000000000000-3-1-110000-11-111-11-1
χ2533-3-1-13333-3-3-3-310000-3-3-1-1-1-111110000000000000000311-10000i−i−ii−iii−i
χ2633-3-1-13333-3-3-3-310000-3-3-1-1-1-111110000000000000000311-10000−iii−ii−i−ii
χ27444441-21-211-2-244444001-21-211-2-211-2-211-2-211-2-211-2-20000000000000000
χ28444441-21-211-2-24-2-2-2-2001-21-211-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i32110000000000000000
χ29444441-21-211-2-24-2-2-2-2001-21-211-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i32110000000000000000
χ3044444-21-21-2-2114444400-21-21-2-211-2-211-2-211-2-211-2-2110000000000000000
χ3144444-21-21-2-2114-2-2-2-200-21-21-2-21111−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i3211−1−3i32−1+3i320000000000000000
χ3244444-21-21-2-2114-2-2-2-200-21-21-2-21111−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i3211−1+3i32−1−3i320000000000000000
χ3344-4441-21-2-1-122-44-4-44001-21-2-1-12211-2-211-2-2-1-122-1-1220000000000000000
χ3444-4441-21-2-1-122-4-222-2001-21-2-1-122−1−3i32−1+3i3211−1−3i32−1+3i32111+3i321−3i32-1-11+3i321−3i32-1-10000000000000000
χ3544-4441-21-2-1-122-4-222-2001-21-2-1-122−1+3i32−1−3i3211−1+3i32−1−3i32111−3i321+3i32-1-11−3i321+3i32-1-10000000000000000
χ3644-444-21-2122-1-1-44-4-4400-21-2122-1-1-2-211-2-21122-1-122-1-10000000000000000
χ3744-444-21-2122-1-1-4-222-200-21-2122-1-111−1−3i32−1+3i3211−1−3i32−1+3i32-1-11+3i321−3i32-1-11+3i321−3i320000000000000000
χ3844-444-21-2122-1-1-4-222-200-21-2122-1-111−1+3i32−1−3i3211−1+3i32−1−3i32-1-11−3i321+3i32-1-11−3i321+3i320000000000000000
χ394-404-41-2-123-3000400-4001-2-123-30011-2-2-1-1223-300-33000000000000000000
χ404-404-41-2-123-3000-2−2i32i32001-2-123-300−1−3i32−1+3i32111+3i321−3i32-1-1−3−i323−i32i3i33+i32−3+i32−i3−i30000000000000000
χ414-404-41-2-123-3000-22i3−2i32001-2-123-300−1+3i32−1−3i32111−3i321+3i32-1-1−3+i323+i32−i3−i33−i32−3−i32i3i30000000000000000
χ424-404-41-2-12-33000400-4001-2-12-330011-2-2-1-122-33003-3000000000000000000
χ434-404-41-2-12-33000-2−2i32i32001-2-12-3300−1+3i32−1−3i32111−3i321+3i32-1-13−i32−3−i32i3i3−3+i323+i32−i3−i30000000000000000
χ444-404-41-2-12-33000-22i3−2i32001-2-12-3300−1−3i32−1+3i32111+3i321−3i32-1-13+i32−3+i32−i3−i3−3−i323−i32i3i30000000000000000
χ454-404-4-212-1003-30400-400-212-1003-3-2-21122-1-1003-300-330000000000000000
χ464-404-4-212-1003-30-2−2i32i3200-212-1003-311−1−3i32−1+3i32-1-11+3i321−3i32i3i3−3−i323−i32−i3−i33+i32−3+i320000000000000000
χ474-404-4-212-1003-30-22i3−2i3200-212-1003-311−1+3i32−1−3i32-1-11−3i321+3i32−i3−i3−3+i323+i32i3i33−i32−3−i320000000000000000
χ484-404-4-212-100-330400-400-212-100-33-2-21122-1-100-33003-30000000000000000
χ494-404-4-212-100-330-2−2i32i3200-212-100-3311−1+3i32−1−3i32-1-11−3i321+3i32i3i33−i32−3−i32−i3−i3−3+i323+i320000000000000000
χ504-404-4-212-100-330-22i3−2i3200-212-100-3311−1−3i32−1+3i32-1-11+3i321−3i32−i3−i33+i32−3+i32i3i3−3−i323−i320000000000000000
χ516-60-2266-6-60000000006i−6i-2-222000000000000000000000−2i2i0000000000000
χ526-60-2266-6-6000000000−6i6i-2-2220000000000000000000002i−2i0000000000000
χ53121212-4-43-63-633-6-6-4000000-12-12-1-12200000000000000000000000000000000
χ54121212-4-4-63-63-6-633-40000002-12-122-1-100000000000000000000000000000000
χ551212-12-4-43-63-6-3-3664000000-12-1211-2-200000000000000000000000000000000
χ561212-12-4-4-63-6366-3-340000002-12-1-2-21100000000000000000000000000000000
χ5712-120-443-6-369-9000000000-121-2-330000000000000000000000000000000000
χ5812-120-443-6-36-99000000000-121-23-30000000000000000000000000000000000
χ5912-120-44-636-3009-900000002-1-2100-3300000000000000000000000000000000
χ6012-120-44-636-300-9900000002-1-21003-300000000000000000000000000000000

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