Finite Group Databasebeta

← Group #10692716

Character table — Group #10692716

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222244444444444488888888161616161616161616161616161616162424242424242424242424244848
order1222344666244444661212121288881212121222666688242424242424242444448888888888
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ911111-1-1111-111-11-1-1-1-1-1-1-1ii−i−i111-11-111-1-1i−iii−i−iii−i−i11-1-1ii−i−i11-1-1i−i
χ1011111-1-1111-111-11-1-1-1-1-1-1-1ii−i−i111-11-111-1-1i−iii−i−iii−i−i-1-111−i−iii-1-111−ii
χ1111111-1-1111-111-11-1-1-1-1-1-1-1ii−i−i111-1-11-1-111−iiii−i−i−i−iii11-1-1ii−i−i-1-111−ii
χ1211111-1-1111-111-11-1-1-1-1-1-1-1ii−i−i111-1-11-1-111−iiii−i−i−i−iii-1-111−i−iii11-1-1i−i
χ1311111-1-1111-111-11-1-1-1-1-1-1-1−i−iii111-11-111-1-1−ii−i−iii−i−iii11-1-1−i−iii11-1-1−ii
χ1411111-1-1111-111-11-1-1-1-1-1-1-1−i−iii111-11-111-1-1−ii−i−iii−i−iii-1-111ii−i−i-1-111i−i
χ1511111-1-1111-111-11-1-1-1-1-1-1-1−i−iii111-1-11-1-111i−i−i−iiiii−i−i11-1-1−i−iii-1-111i−i
χ1611111-1-1111-111-11-1-1-1-1-1-1-1−i−iii111-1-11-1-111i−i−i−iiiii−i−i-1-111ii−i−i11-1-1−ii
χ1722222222222-2-2-22-22222-2-200002-2-2-200000000000000002-22-20000000000
χ1822222222222-2-2-22-22222-2-200002-2-2-20000000000000000-22-220000000000
χ192222222222-22-22-2-2-2-222222-22-2-22-2-2000000002-22-2000000000000000000
χ202222222222-22-22-2-2-2-22222-22-22-22-2-200000000-22-22000000000000000000
χ212222222222-2-22-2-22-2-222-2-20000-2-222000000000000000000002-22-2000000
χ222222222222-2-22-2-22-2-222-2-20000-2-22200000000000000000000-22-22000000
χ2322222-2-222222-2-2-2222-2-2-2-22i−2i−2i2i-22-22000000002i−2i−2i2i000000000000000000
χ2422222-2-222222-2-2-2222-2-2-2-2−2i2i2i−2i-22-2200000000−2i2i2i−2i000000000000000000
χ2522222-2-22222-222-2-222-2-2220000-2-22-2000000000000000000002i−2i−2i2i000000
χ2622222-2-22222-222-2-222-2-2220000-2-22-200000000000000000000−2i2i2i−2i000000
χ2722222-2-2222-2-2-2222-2-2-2-22200002-2-2200000000000000002-2-220000000000
χ2822222-2-2222-2-2-2222-2-2-2-22200002-2-220000000000000000-222-20000000000
χ292222-122-1-1-1222222-1-1-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ302222-122-1-1-1222222-1-1-1-1-1-12222-1-1-1-1-2-21111-2-2-1-1-1-1111100000000000000
χ312222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-2-21111111100000000000000
χ322222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-21111221111-1-1-1-100000000000000
χ332222-122-1-1-1-22-22-2-211-1-1-1-12-22-21-11100−i3i3−i3i300-11-11−i3i3−i3i300000000000000
χ342222-122-1-1-1-22-22-2-211-1-1-1-12-22-21-11100i3−i3i3−i300-11-11i3−i3i3−i300000000000000
χ352222-122-1-1-1-22-22-2-211-1-1-1-1-22-221-11100−i3i3−i3i3001-11-1i3−i3i3−i300000000000000
χ362222-122-1-1-1-22-22-2-211-1-1-1-1-22-221-11100i3−i3i3−i3001-11-1−i3i3−i3i300000000000000
χ372222-1-2-2-1-1-122-2-2-22-1-111112i−2i−2i2i1-11-100−i3i3i3−i300−iii−i3−3−3300000000000000
χ382222-1-2-2-1-1-122-2-2-22-1-111112i−2i−2i2i1-11-100i3−i3−i3i300−iii−i−333−300000000000000
χ392222-1-2-2-1-1-122-2-2-22-1-11111−2i2i2i−2i1-11-100−i3i3i3−i300i−i−ii−333−300000000000000
χ402222-1-2-2-1-1-122-2-2-22-1-11111−2i2i2i−2i1-11-100i3−i3−i3i300i−i−ii3−3−3300000000000000
χ412222-1-2-2-1-1-1-222-22-21111112i2i−2i−2i-1-1-112-2-1-1112i−2i−i−iii−i−iii00000000000000
χ422222-1-2-2-1-1-1-222-22-21111112i2i−2i−2i-1-1-11-2211-1-1−2i2i−i−iiiii−i−i00000000000000
χ432222-1-2-2-1-1-1-222-22-2111111−2i−2i2i2i-1-1-112-2-1-111−2i2iii−i−iii−i−i00000000000000
χ442222-1-2-2-1-1-1-222-22-2111111−2i−2i2i2i-1-1-11-2211-1-12i−2iii−i−i−i−iii00000000000000
χ454444-244-2-2-24-4-4-44-4-2-2-2-2220000-2222000000000000000000000000000000
χ464444-244-2-2-2-4-44-4-4422-2-222000022-2-2000000000000000000000000000000
χ474444-2-4-4-2-2-24-444-4-4-2-222-2-2000022-22000000000000000000000000000000
χ484444-2-4-4-2-2-2-4-4-44442222-2-20000-222-2000000000000000000000000000000
χ4944-4-444-44-4-4000000004-400000000000000000000000000000000002i−2i2i−2i00
χ5044-4-444-44-4-4000000004-40000000000000000000000000000000000−2i2i−2i2i00
χ5144-4-44-444-4-400000000-4400000000000000000000000000000000002i−2i−2i2i00
χ5244-4-44-444-4-400000000-440000000000000000000000000000000000−2i2i2i−2i00
χ5388-8-8-48-8-44400000000-440000000000000000000000000000000000000000
χ5488-8-8-4-88-444000000004-40000000000000000000000000000000000000000
χ558-88-8800-88-800000000000000000000000000000000000000000000000000
χ568-88-8-4004-44000000−4i34i3000000000000000000000000000000000000000000
χ578-88-8-4004-440000004i3−4i3000000000000000000000000000000000000000000
χ588-8-88800-8-8800000000000000000000000000000000000000000000000000
χ598-8-88-40044-40000000000−4i34i300000000000000000000000000000000000000
χ608-8-88-40044-400000000004i3−4i300000000000000000000000000000000000000

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