Finite Group Databasebeta

← Group #13167420

Character table — Group #13167420

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222224444444444888888888888888888889918181818181818363636363636363636363636363636363636363636367272727272727272
order12234466633661212121212123366666666121212121212121212122224466662244444488881212121212121212121266121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-1ii−i−iii−i−i11iiii−i−i−i−i1-11-1ii−i−i
χ61111-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-1−i−iii−i−iii11−i−i−i−iiiii1-11-1−i−iii
χ71111-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-11ii−i−i−i−iii11iiii−i−i−i−i-11-11−i−iii
χ81111-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-11−i−iiiii−i−i11−i−i−i−iiiii-11-11ii−i−i
χ911-111-1-1-1111111-111-1-111-1-1-1-1-1-1111-11111-1-1-1-1-1-111-111-1-11-1-11i−ii−ii−ii−i1-1ii−i−iii−i−i1-1-11i−ii−i
χ1011-111-1-1-1111111-111-1-111-1-1-1-1-1-1111-11111-1-1-1-1-1-111-111-1-11-1-11−ii−ii−ii−ii1-1−i−iii−i−iii1-1-11−ii−ii
χ1111-111-1-1-1111111-111-1-111-1-1-1-1-1-1111-11111-1-1-1-1-1-111-111-1-1-111-1i−ii−i−ii−ii1-1ii−i−iii−i−i-111-1−ii−ii
χ1211-111-1-1-1111111-111-1-111-1-1-1-1-1-1111-11111-1-1-1-1-1-111-111-1-1-111-1−ii−iii−ii−i1-1−i−iii−i−iii-111-1i−ii−i
χ1311-11-11-1-111111-11-1-11111-1-1-1-1-1-111-11-1-1-1-1111111-11-1-1-11111-1-11-1-111-1-111-111-1-1-1-11111-1-11-1-11
χ1411-11-11-1-111111-11-1-11111-1-1-1-1-1-111-11-1-1-1-1111111-11-1-1-11111-1-1-111-1-111-11-1-1-11111-1-111-1-1-111-1
χ1511-11-11-1-111111-11-1-11111-1-1-1-1-1-111-11-1-1-1-1111111-11-1-1-111-1-1111-1-11-111-11-111-1-1-1-111-1-111-111-1
χ1611-11-11-1-111111-11-1-11111-1-1-1-1-1-111-11-1-1-1-1111111-11-1-1-111-1-111-111-11-1-111-1-1-11111-1-1-1-1111-1-11
χ17222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2000000000000-2-20000000000000000
χ182222-2-22222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2222-2-22222000000000000-2-20000000000000000
χ19222-122-1-1-12222-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-1000022220000-1-1-1-1-1-1-1-1-1-100000000
χ20222-122-1-1-12222-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-10000-2-2-2-20000-1-11111111100000000
χ21222-122-1-1-12222-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-21111000000000000113−33−33−33−300000000
χ22222-122-1-1-12222-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2111100000000000011−33−33−33−3300000000
χ23222-1-2-2-1-1-1222211-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111222-2-2-1-1-1-100000000000011−i3i3−i3i3i3−i3i3−i300000000
χ24222-1-2-2-1-1-1222211-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111222-2-2-1-1-1-100000000000011i3−i3i3−i3−i3i3−i3i300000000
χ25222-1-2-2-1-1-1222211-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111-2-2-222111100002i2i−2i−2i0000-1-1−i−i−i−iiiii00000000
χ26222-1-2-2-1-1-1222211-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111-2-2-22211110000−2i−2i2i2i0000-1-1iiii−i−i−i−i00000000
χ2722-222-2-2-2222222-222-2-222-2-2-2-2-2-2222-22222-2-2-2-222-2-22-2-222000000000000-220000000000000000
χ2822-22-22-2-222222-22-2-22222-2-2-2-2-2-222-22-2-2-2-22222-2-22-2222-2-2000000000000-220000000000000000
χ2922-2-12-211-12222-1122-2-2-1-1-2-21111-1-12-2-1-1-1-1111122-2-2211-1-10000000000001-1−i3i3i3−i3−i3i3i3−i300000000
χ3022-2-12-211-12222-1122-2-2-1-1-2-21111-1-12-2-1-1-1-1111122-2-2211-1-10000000000001-1i3−i3−i3i3i3−i3−i3i300000000
χ3122-2-12-211-12222-1122-2-2-1-1-2-21111-1-12-2-1-1-1-11111-2-222-2-1-11100002i−2i2i−2i0000-11−i−iii−i−iii00000000
χ3222-2-12-211-12222-1122-2-2-1-1-2-21111-1-12-2-1-1-1-11111-2-222-2-1-1110000−2i2i−2i2i0000-11ii−i−iii−i−i00000000
χ3322-2-1-2211-122221-1-2-222-1-1-2-21111-1-1-221111-1-1-1-122-22-211-1-100002-2-220000-11-1-11111-1-100000000
χ3422-2-1-2211-122221-1-2-222-1-1-2-21111-1-1-221111-1-1-1-122-22-211-1-10000-222-20000-1111-1-1-1-11100000000
χ3522-2-1-2211-122221-1-2-222-1-1-2-21111-1-1-221111-1-1-1-1-2-22-22-1-1110000000000001-13−3−33−333−300000000
χ3622-2-1-2211-122221-1-2-222-1-1-2-21111-1-1-221111-1-1-1-1-2-22-22-1-1110000000000001-1−333−33−3−3300000000
χ374444444441-21-244-2-2111-21-211-2-21-21-211-2-211-2-200000000000000000222200000000000000-1-1-1-1
χ384444444441-21-244-2-2111-21-211-2-21-21-211-2-211-2-200000000000000000-2-2-2-2000000000000001111
χ39444444444-21-214411-2-2-21-21-2-211-21-21-2-211-2-2110000000002222000000000000000000-1-1-1-10000
χ40444444444-21-214411-2-2-21-21-2-211-21-21-2-211-2-211000000000-2-2-2-200000000000000000011110000
χ414444-4-44441-21-2-4-422-1-11-21-211-2-21-2-12-1-122-1-122000000000000000002i2i−2i−2i00000000000000−i−iii
χ424444-4-44441-21-2-4-422-1-11-21-211-2-21-2-12-1-122-1-12200000000000000000−2i−2i2i2i00000000000000ii−i−i
χ434444-4-4444-21-21-4-4-1-122-21-21-2-211-212-122-1-122-1-10000000002-22-2000000000000000000-11-110000
χ444444-4-4444-21-21-4-4-1-122-21-21-2-211-212-122-1-122-1-1000000000-22-220000000000000000001-11-10000
χ4544-444-4-4-441-21-24-4-2-2-1-11-2-12-1-1221-21211-2-2-1-122000000000000000002i−2i2i−2i00000000000000−ii−ii
χ4644-444-4-4-441-21-24-4-2-2-1-11-2-12-1-1221-21211-2-2-1-12200000000000000000−2i2i−2i2i00000000000000i−ii−i
χ4744-444-4-4-44-21-214-41122-212-122-1-1-21-2-1-2-21122-1-10000000002-2-22000000000000000000-111-10000
χ4844-444-4-4-44-21-214-41122-212-122-1-1-21-2-1-2-21122-1-1000000000-222-20000000000000000001-1-110000
χ4944-44-44-4-441-21-2-4422111-2-12-1-1221-2-1-2-1-12211-2-2000000000000000002-2-2200000000000000-111-1
χ5044-44-44-4-441-21-2-4422111-2-12-1-1221-2-1-2-1-12211-2-200000000000000000-222-2000000000000001-1-11
χ5144-44-44-4-44-21-21-44-1-1-2-2-212-122-1-1-212122-1-1-2-21100000000022-2-2000000000000000000-1-1110000
χ5244-44-44-4-44-21-21-44-1-1-2-2-212-122-1-1-212122-1-1-2-211000000000-2-22200000000000000000011-1-10000
χ534-4040000-444-4-400000044000000-4-400000000004-4000004-4000000000000000000000000000000
χ544-4040000-444-4-400000044000000-4-40000000000-4400000-44000000000000000000000000000000
χ554-40-200−2i32i3244-4-4000000-2-200−2i32i3−2i32i32200000000004-4000−2i32i3-22000000000000000000000000000000
χ564-40-200−2i32i3244-4-4000000-2-200−2i32i3−2i32i3220000000000-440002i3−2i32-2000000000000000000000000000000
χ574-40-2002i3−2i3244-4-4000000-2-2002i3−2i32i3−2i32200000000004-40002i3−2i3-22000000000000000000000000000000
χ584-40-2002i3−2i3244-4-4000000-2-2002i3−2i32i3−2i3220000000000-44000−2i32i32-2000000000000000000000000000000
χ59888-488-4-4-42-42-4-4-4-4-422-122-4-1-122-122-4-1-122-1-122000000000000000000000000000000000000000
χ60888-488-4-4-4-42-42-4-422-4-42-1-4222-1-12-1-4222-1-122-1-1000000000000000000000000000000000000000
χ61888-4-8-8-4-4-42-42-44444-2-2-122-4-1-122-12-2411-2-211-2-2000000000000000000000000000000000000000
χ62888-4-8-8-4-4-4-42-4244-2-2442-1-4222-1-12-14-2-2-211-2-211000000000000000000000000000000000000000
χ6388-8-48-844-42-42-4-44-4-4-2-2-12-2411-2-2-1224-1-12211-2-2000000000000000000000000000000000000000
χ6488-8-48-844-4-42-42-4422442-14-2-2-2112-1-4-222-1-1-2-211000000000000000000000000000000000000000
χ6588-8-4-8844-42-42-44-44422-12-2411-2-2-12-2-411-2-2-1-122000000000000000000000000000000000000000
χ6688-8-4-8844-4-42-424-4-2-2-4-42-14-2-2-2112-142-2-21122-1-1000000000000000000000000000000000000000
χ678-8080000-82-4-2400006i−6i2-4000000-240000006i−6i00000000000000000000000000000000000000000
χ688-8080000-82-4-240000−6i6i2-4000000-24000000−6i6i00000000000000000000000000000000000000000
χ698-8080000-8-424-2006i−6i00-420000004-200006i−6i0000000000000000000000000000000000000000000
χ708-8080000-8-424-200−6i6i00-420000004-20000−6i6i0000000000000000000000000000000000000000000
χ718-80-400−4i34i342-4-2400006i−6i-1200−i3i32i3−2i31-20033−3300−3i3i00000000000000000000000000000000000000000
χ728-80-400−4i34i342-4-240000−6i6i-1200−i3i32i3−2i31-200−3333003i−3i00000000000000000000000000000000000000000
χ738-80-400−4i34i34-424-2006i−6i002-1002i3−2i3−i3i3-210000−3i3i0033−33000000000000000000000000000000000000000
χ748-80-400−4i34i34-424-200−6i6i002-1002i3−2i3−i3i3-2100003i−3i00−3333000000000000000000000000000000000000000
χ758-80-4004i3−4i342-4-2400006i−6i-1200i3−i3−2i32i31-200−333300−3i3i00000000000000000000000000000000000000000
χ768-80-4004i3−4i342-4-240000−6i6i-1200i3−i3−2i32i31-20033−33003i−3i00000000000000000000000000000000000000000
χ778-80-4004i3−4i34-424-2006i−6i002-100−2i32i3i3−i3-210000−3i3i00−3333000000000000000000000000000000000000000
χ788-80-4004i3−4i34-424-200−6i6i002-100−2i32i3i3−i3-2100003i−3i0033−33000000000000000000000000000000000000000

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