Finite Group Databasebeta

← Group #10692674

Character table — Group #10692674

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222244444444444488888888161616161616161616161616161616162424242424242424242424244848
order122234466624444466121212122244121212124466881212121212122424242488888888888824
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ911111-1-1111-111-1-11-1-1-1-1-1-111-1-111-11i−i11i−i-1-1ii−i−iii−i−iii−i−iii−i−i11-1-11-1
χ1011111-1-1111-111-1-11-1-1-1-1-1-111-1-111-11i−i11i−i-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-11
χ1111111-1-1111-111-1-11-1-1-1-1-1-111-1-111-11−ii11−ii-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-11
χ1211111-1-1111-111-1-11-1-1-1-1-1-111-1-111-11−ii11−ii-1-1−i−iii−i−iii−i−iii−i−iii11-1-11-1
χ1311111-1-1111-111-1-11-1-1-1-1-1-1-1-11111-11i−i-1-1−ii11ii−i−i−i−iiiii−i−i−i−iii11-1-1-11
χ1411111-1-1111-111-1-11-1-1-1-1-1-1-1-11111-11i−i-1-1−ii11ii−i−i−i−iii−i−iiiii−i−i-1-1111-1
χ1511111-1-1111-111-1-11-1-1-1-1-1-1-1-11111-11−ii-1-1i−i11−i−iiiii−i−iii−i−i−i−iii-1-1111-1
χ1611111-1-1111-111-1-11-1-1-1-1-1-1-1-11111-11−ii-1-1i−i11−i−iiiii−i−i−i−iiiii−i−i11-1-1-11
χ17222222222222-2-2-2-22222-2-20000-2-2-22000000000000000000002-22-2000000
χ18222222222222-2-2-2-22222-2-20000-2-2-2200000000000000000000-22-22000000
χ192222222222-2-22-22-2-2-2222200002-2-2-200000000000000002-22-20000000000
χ202222222222-2-22-22-2-2-2222200002-2-2-20000000000000000-22-220000000000
χ212222222222-2-2-22-22-2-222-2-22-22-2-222-2002-2002-20000000000000000000000
χ222222222222-2-2-22-22-2-222-2-2-22-22-222-200-2200-220000000000000000000000
χ2322222-2-22222-222-2-222-2-2-2-200002-22-200000000000000002i−2i−2i2i0000000000
χ2422222-2-22222-222-2-222-2-2-2-200002-22-20000000000000000−2i2i2i−2i0000000000
χ2522222-2-22222-2-2-22222-2-2222-2-22-22-2-2002-200-220000000000000000000000
χ2622222-2-22222-2-2-22222-2-222-222-2-22-2-200-22002-20000000000000000000000
χ2722222-2-2222-22-222-2-2-2-2-2220000-2-222000000000000000000002i−2i−2i2i000000
χ2822222-2-2222-22-222-2-2-2-2-2220000-2-22200000000000000000000−2i2i2i−2i000000
χ292222-122-1-1-1222222-1-1-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000000000
χ302222-122-1-1-1222222-1-1-1-1-1-12222-1-1-1-1-2-2-1-1-2-2-1-11111111100000000000000
χ312222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-1-1-1-12211-2-211-1-1-1-1111100000000000000
χ322222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-21122111111-1-1-1-100000000000000
χ332222-122-1-1-1-2-2-22-2211-1-1112-22-21-1-1100-1100-113−33−33−33−300000000000000
χ342222-122-1-1-1-2-2-22-2211-1-1112-22-21-1-1100-1100-11−33−33−33−3300000000000000
χ352222-122-1-1-1-2-2-22-2211-1-111-22-221-1-11001-1001-13−33−3−33−3300000000000000
χ362222-122-1-1-1-2-2-22-2211-1-111-22-221-1-11001-1001-1−33−333−33−300000000000000
χ372222-1-2-2-1-1-12-2-2-222-1-111-1-12-2-221-11100-11001-1−i3i3i3−i3−i3i3i3−i300000000000000
χ382222-1-2-2-1-1-12-2-2-222-1-111-1-12-2-221-11100-11001-1i3−i3−i3i3i3−i3−i3i300000000000000
χ392222-1-2-2-1-1-12-2-2-222-1-111-1-1-222-21-111001-100-11−i3i3i3−i3i3−i3−i3i300000000000000
χ402222-1-2-2-1-1-12-2-2-222-1-111-1-1-222-21-111001-100-11i3−i3−i3i3−i3i3i3−i300000000000000
χ412222-1-2-2-1-1-1-222-2-2211111122-2-2-1-11-12i−2i-1-12i−2i11−i−iii−i−iii00000000000000
χ422222-1-2-2-1-1-1-222-2-2211111122-2-2-1-11-1−2i2i-1-1−2i2i11ii−i−iii−i−i00000000000000
χ432222-1-2-2-1-1-1-222-2-22111111-2-222-1-11-12i−2i11−2i2i-1-1−i−iiiii−i−i00000000000000
χ442222-1-2-2-1-1-1-222-2-22111111-2-222-1-11-1−2i2i112i−2i-1-1ii−i−i−i−iii00000000000000
χ454444-244-2-2-244-4-4-4-4-2-2-2-2220000222-2000000000000000000000000000000
χ464444-244-2-2-2-4-44-44-422-2-2-2-20000-2222000000000000000000000000000000
χ474444-2-4-4-2-2-24-444-4-4-2-222220000-22-22000000000000000000000000000000
χ484444-2-4-4-2-2-2-44-444-42222-2-2000022-2-2000000000000000000000000000000
χ4944-4-444i−4i4-4-4000000004i−4i00000000000000000000000000000000002-22i−2i00
χ5044-4-444i−4i4-4-4000000004i−4i0000000000000000000000000000000000-22−2i2i00
χ5144-4-44−4i4i4-4-400000000−4i4i00000000000000000000000000000000002-2−2i2i00
χ5244-4-44−4i4i4-4-400000000−4i4i0000000000000000000000000000000000-222i−2i00
χ5388-8-8-48i−8i-44400000000−4i4i0000000000000000000000000000000000000000
χ5488-8-8-4−8i8i-444000000004i−4i0000000000000000000000000000000000000000
χ558-88-8800-8-8800000000000000000000000000000000000000000000000000
χ568-88-8-40044-4000000−4i34i3000000000000000000000000000000000000000000
χ578-88-8-40044-40000004i3−4i3000000000000000000000000000000000000000000
χ588-8-88800-88-800000000000000000000000000000000000000000000000000
χ598-8-88-4004-44000000000043−4300000000000000000000000000000000000000
χ608-8-88-4004-440000000000−434300000000000000000000000000000000000000

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