Finite Group Databasebeta

← Group #10693267

Character table — Group #10693267

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112222222244444444444888888881212121216161616161616161616161616161616242424242424242424244848
order122234444666244441212121212124444612121288888888121212122424242424242424444488888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ511111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ911111-1-1-1-11111-11-11-1-1-1-1-1-11-11-1111-1ii−i−ii−ii−i11-1-1ii−i−iii−i−i11-1-1i−iii−i−i1-1
χ1011111-1-1-1-11111-11-11-1-1-1-1-1-11-11-1111-1ii−i−i−ii−ii11-1-1−i−iii−i−iii-1-111i−iii−i−i-11
χ1111111-1-1-1-11111-11-11-1-1-1-1-1-11-11-1111-1−i−iiii−ii−i11-1-1ii−i−iii−i−i-1-111−ii−i−iii-11
χ1211111-1-1-1-11111-11-11-1-1-1-1-1-11-11-1111-1−i−iii−ii−ii11-1-1−i−iii−i−iii11-1-1−ii−i−iii1-1
χ1311111-1-1-1-11111-11-11-1-1-1-1-1-1-11-11111-1ii−i−ii−i−ii-1-111−i−iiiii−i−i11-1-1i−i−i−iii-11
χ1411111-1-1-1-11111-11-11-1-1-1-1-1-1-11-11111-1ii−i−i−iii−i-1-111ii−i−i−i−iii-1-111i−i−i−iii1-1
χ1511111-1-1-1-11111-11-11-1-1-1-1-1-1-11-11111-1−i−iiii−i−ii-1-111−i−iiiii−i−i-1-111−iiii−i−i1-1
χ1611111-1-1-1-11111-11-11-1-1-1-1-1-1-11-11111-1−i−iii−iii−i-1-111ii−i−i−i−iii11-1-1−iiii−i−i-11
χ17222222222222-2-22-2-2222-2-220000-22-2-2222200000000000000000000-2-2000000
χ18222222222222-2-22-2-2222-2-220000-22-2-2-2-2-2-20000000000000000000022000000
χ192222222-2-222222-2-2-2-2-22-2-2200002-2-22000000000000000000000000002i−2i2i−2i00
χ202222222-2-222222-2-2-2-2-22-2-2200002-2-2200000000000000000000000000−2i2i−2i2i00
χ212222222-2-2222-2-2-222-2-2222222-2-2-2-22-2000000002-22-200000000000000000000
χ222222222-2-2222-2-2-222-2-22222-2-222-2-22-200000000-22-2200000000000000000000
χ2322222-2-2222222-2-22-222-222-200002-2-2-2000000000000000000000000002-2-2200
χ2422222-2-2222222-2-22-222-222-200002-2-2-200000000000000000000000000-222-200
χ2522222-2-222222-22-2-2222-2-2-2-22-2-22-2-222000000002-2-2200000000000000000000
χ2622222-2-222222-22-2-2222-2-2-2-2-222-2-2-22200000000-222-200000000000000000000
χ2722222-2-2-2-2222-2222-2-2-2-222-20000-22-222i2i−2i−2i00000000000000000000−2i2i000000
χ2822222-2-2-2-2222-2222-2-2-2-222-20000-22-22−2i−2i2i2i000000000000000000002i−2i000000
χ292222-12222-1-1-122222-1-1-1-1-1-12222-1-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ302222-12222-1-1-122222-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-1-1-1-111111111000000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-211111111-1-1-1-1000000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-2221111-1-1-1-11111000000000000
χ332222-122-2-2-1-1-1-2-2-22211-1-1-1-122-2-211-1100000000-11-11−i3i3−i3i3−i3i3−i3i3000000000000
χ342222-122-2-2-1-1-1-2-2-22211-1-1-1-122-2-211-1100000000-11-11i3−i3i3−i3i3−i3i3−i3000000000000
χ352222-122-2-2-1-1-1-2-2-22211-1-1-1-1-2-22211-11000000001-11-1−i3i3−i3i3i3−i3i3−i3000000000000
χ362222-122-2-2-1-1-1-2-2-22211-1-1-1-1-2-22211-11000000001-11-1i3−i3i3−i3−i3i3−i3i3000000000000
χ372222-1-2-222-1-1-1-22-2-22-1-111112-2-2211-1-100000000-111-13−3−333−3−33000000000000
χ382222-1-2-222-1-1-1-22-2-22-1-111112-2-2211-1-100000000-111-1−333−3−333−3000000000000
χ392222-1-2-222-1-1-1-22-2-22-1-11111-222-211-1-1000000001-1-113−3−33−333−3000000000000
χ402222-1-2-222-1-1-1-22-2-22-1-11111-222-211-1-1000000001-1-11−333−33−3−33000000000000
χ412222-1-2-2-2-2-1-1-12-22-221111112-22-2-1-1-1100002i−2i2i−2i-1-111−i−iii−i−iii000000000000
χ422222-1-2-2-2-2-1-1-12-22-221111112-22-2-1-1-110000−2i2i−2i2i-1-111ii−i−iii−i−i000000000000
χ432222-1-2-2-2-2-1-1-12-22-22111111-22-22-1-1-1100002i−2i−2i2i11-1-1ii−i−i−i−iii000000000000
χ442222-1-2-2-2-2-1-1-12-22-22111111-22-22-1-1-110000−2i2i2i−2i11-1-1−i−iiiii−i−i000000000000
χ454444-24444-2-2-2-4-44-4-4-2-2-222-200002-22200000000000000000000000000000000
χ464444-244-4-4-2-2-244-4-4-422-222-20000-222-200000000000000000000000000000000
χ474444-2-4-444-2-2-24-4-44-4-2-22-2-220000-222200000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-2-4444-4222-2-2200002-22-200000000000000000000000000000000
χ4944-4-444-400-44-40000000400-40000000022−2222−220000000000000000000000000000
χ5044-4-444-400-44-40000000400-400000000−2222−22220000000000000000000000000000
χ5144-4-44-4400-44-40000000-400400000000−2i22i22i2−2i20000000000000000000000000000
χ5244-4-44-4400-44-40000000-4004000000002i2−2i2−2i22i20000000000000000000000000000
χ534-4-444004i−4i-4-44000004i−4i000000000000000000000000000000002i−2i2-200000000
χ544-4-444004i−4i-4-44000004i−4i00000000000000000000000000000000−2i2i-2200000000
χ554-4-44400−4i4i-4-4400000−4i4i000000000000000000000000000000002i−2i-2200000000
χ564-4-44400−4i4i-4-4400000−4i4i00000000000000000000000000000000−2i2i2-200000000
χ5788-8-8-48-8004-440000000-40040000000000000000000000000000000000000000
χ5888-8-8-4-88004-440000000400-40000000000000000000000000000000000000000
χ598-88-8800008-8-8000000000000000000000000000000000000000000000000000
χ608-88-8-40000-44400000000−4i34i300000000000000000000000000000000000000000
χ618-88-8-40000-444000000004i3−4i300000000000000000000000000000000000000000
χ628-8-88-4008i−8i44-400000−4i4i00000000000000000000000000000000000000000000
χ638-8-88-400−8i8i44-4000004i−4i00000000000000000000000000000000000000000000

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