Finite Group Databasebeta

← Group #10830072

Character table — Group #10830072

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order1222222234444666666644444444121212121212121212121212222244666666668888121212121212121224242424242424244444222244888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ7111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1
χ8111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ911111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-111-1-11-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-1-111-11
χ1111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-11-1-1-111-11
χ1211111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-111-1111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11-1-1111-1
χ17222222222-2-2-2-2222222222-2-20000-2-22222-2-2-2-2-2-2000000000000000000000000000000000022220000-2-2000000
χ18222222222-2-2-2-2222222222-2-20000-2-22222-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-2000022000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-22222-2-2000000000000000000000000000000000022-2-20000-22000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-22200002-2000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111-2-2-2-2-1-1-1-11111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-21111-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-2-222-2-21111-1-1-1-122-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-2-2-2-22211111111-2-222-1-1-1-1-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-12222-2-2-1-1-1-1-1-1-1-1-2-222111111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-122-2-222-1-1-1-1111122-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ292222-2-2-2-22-22-2222-2-22-2-200002i2i−2i−2i2-2000000002-2002-200000022-2-22i−2i002i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ302222-2-2-2-22-22-2222-2-22-2-200002i2i−2i−2i2-2000000002-200-22000000-2-222−2i2i002i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ312222-2-2-2-22-22-2222-2-22-2-20000−2i−2i2i2i2-2000000002-2002-200000022-2-2−2i2i00−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ322222-2-2-2-22-22-2222-2-22-2-20000−2i−2i2i2i2-2000000002-200-22000000-2-2222i−2i00−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ332222-2-2-2-2-1-22-22-1-111-11100002i2i−2i−2i-1133−3−333−3−3-11002-200−i3−i3i3i3-1-1112i−2i00−i−iii33−3−3−i−iii−i3−i3i3i30000000000000000
χ342222-2-2-2-2-1-22-22-1-111-11100002i2i−2i−2i-1133−3−333−3−3-1100-2200−i3−i3i3i311-1-1−2i2i00−i−iii−3−333ii−i−ii3i3−i3−i30000000000000000
χ352222-2-2-2-2-1-22-22-1-111-11100002i2i−2i−2i-11−3−333−3−333-11002-200i3i3−i3−i3-1-1112i−2i00−i−iii−3−333−i−iiii3i3−i3−i30000000000000000
χ362222-2-2-2-2-1-22-22-1-111-11100002i2i−2i−2i-11−3−333−3−333-1100-2200i3i3−i3−i311-1-1−2i2i00−i−iii33−3−3ii−i−i−i3−i3i3i30000000000000000
χ372222-2-2-2-2-1-22-22-1-111-1110000−2i−2i2i2i-1133−3−333−3−3-11002-200i3i3−i3−i3-1-111−2i2i00ii−i−i33−3−3ii−i−ii3i3−i3−i30000000000000000
χ382222-2-2-2-2-1-22-22-1-111-1110000−2i−2i2i2i-1133−3−333−3−3-1100-2200i3i3−i3−i311-1-12i−2i00ii−i−i−3−333−i−iii−i3−i3i3i30000000000000000
χ392222-2-2-2-2-1-22-22-1-111-1110000−2i−2i2i2i-11−3−333−3−333-11002-200−i3−i3i3i3-1-111−2i2i00ii−i−i−3−333ii−i−i−i3−i3i3i30000000000000000
χ402222-2-2-2-2-1-22-22-1-111-1110000−2i−2i2i2i-11−3−333−3−333-1100-2200−i3−i3i3i311-1-12i−2i00ii−i−i33−3−3−i−iiii3i3−i3−i30000000000000000
χ412-2-2222-2-2222-2-2-2-2222-2-200002i−2i2i−2i-22000000002-200002i−2i00000000002-22i−2i2i−2i2i−2i2i−2i00002-22-20000000000000000
χ422-2-2222-2-2222-2-2-2-2222-2-200002i−2i2i−2i-22000000002-20000−2i2i0000000000-222i−2i2i−2i−2i2i−2i2i0000-22-220000000000000000
χ432-2-2222-2-2222-2-2-2-2222-2-20000−2i2i−2i2i-22000000002-200002i−2i0000000000-22−2i2i−2i2i2i−2i2i−2i0000-22-220000000000000000
χ442-2-2222-2-2222-2-2-2-2222-2-20000−2i2i−2i2i-22000000002-20000−2i2i00000000002-2−2i2i−2i2i−2i2i−2i2i00002-22-20000000000000000
χ452-2-2222-2-2-122-2-211-1-1-11100002i−2i2i−2i1-13−33−33−33−3-1100002i−2i−i3i3−i3i3−i3i3−i3i3002-2−ii−ii−ii−ii3−33−3-11-110000000000000000
χ462-2-2222-2-2-122-2-211-1-1-11100002i−2i2i−2i1-13−33−33−33−3-110000−2i2i−i3i3−i3i3i3−i3i3−i300-22−ii−iii−ii−i−33−331-11-10000000000000000
χ472-2-2222-2-2-122-2-211-1-1-11100002i−2i2i−2i1-1−33−33−33−33-1100002i−2ii3−i3i3−i3i3−i3i3−i3002-2−ii−ii−ii−ii−33−33-11-110000000000000000
χ482-2-2222-2-2-122-2-211-1-1-11100002i−2i2i−2i1-1−33−33−33−33-110000−2i2ii3−i3i3−i3−i3i3−i3i300-22−ii−iii−ii−i3−33−31-11-10000000000000000
χ492-2-2222-2-2-122-2-211-1-1-1110000−2i2i−2i2i1-13−33−33−33−3-1100002i−2ii3−i3i3−i3−i3i3−i3i300-22i−ii−i−ii−ii−33−331-11-10000000000000000
χ502-2-2222-2-2-122-2-211-1-1-1110000−2i2i−2i2i1-13−33−33−33−3-110000−2i2ii3−i3i3−i3i3−i3i3−i3002-2i−ii−ii−ii−i3−33−3-11-110000000000000000
χ512-2-2222-2-2-122-2-211-1-1-1110000−2i2i−2i2i1-1−33−33−33−33-1100002i−2i−i3i3−i3i3i3−i3i3−i300-22i−ii−i−ii−ii3−33−31-11-10000000000000000
χ522-2-2222-2-2-122-2-211-1-1-1110000−2i2i−2i2i1-1−33−33−33−33-110000−2i2i−i3i3−i3i3−i3i3−i3i3002-2i−ii−ii−ii−i−33−33-11-110000000000000000
χ532-2-22-2-22222-2-22-2-2-2-22222-22-20000222-2-22-222-2-2-2000000000000000000000000000000000000002-22-200000000
χ542-2-22-2-22222-2-22-2-2-2-22222-22-20000222-2-22-222-2-2-200000000000000000000000000000000000000-22-2200000000
χ552-2-22-2-22222-2-22-2-2-2-2222-22-22000022-222-22-2-22-2-2000000000000000000000000000000000000002-2-2200000000
χ562-2-22-2-22222-2-22-2-2-2-2222-22-22000022-222-22-2-22-2-200000000000000000000000000000000000000-222-200000000
χ572-2-22-2-2222-222-2-2-2-2-22222-2-222-2-22-2-22-2-222-2-22222-200002-2-22000000002-2-220000000000000000000000000000
χ582-2-22-2-2222-222-2-2-2-2-22222-2-22-222-2-2-22-2-222-2-2222-220000-222-200000000-222-20000000000000000000000000000
χ592-2-22-2-2222-222-2-2-2-2-2222-222-22-2-22-2-2-222-2-222-222-220000-222-2000000002-2-220000000000000000000000000000
χ602-2-22-2-2222-222-2-2-2-2-2222-222-2-222-2-2-2-222-2-222-2222-200002-2-2200000000-222-20000000000000000000000000000
χ612-2-22-2-222-1-222-21111-1-1-12-2-222-2-2211-111-1-111-1-1-12-20000-111-1−i3i3i3−i30000-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ622-2-22-2-222-1-222-21111-1-1-12-2-222-2-2211-111-1-111-1-1-12-20000-111-1i3−i3−i3i30000-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ632-2-22-2-222-1-222-21111-1-1-12-2-22-222-211-111-1-111-1-1-1-2200001-1-11−i3i3i3−i300001-1-11−i3i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ642-2-22-2-222-1-222-21111-1-1-12-2-22-222-211-111-1-111-1-1-1-2200001-1-11i3−i3−i3i300001-1-11i3−i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ652-2-22-2-222-1-222-21111-1-1-1-222-22-2-22111-1-111-1-11-1-1-2200001-1-11−i3i3i3−i30000-111-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ662-2-22-2-222-1-222-21111-1-1-1-222-22-2-22111-1-111-1-11-1-1-2200001-1-11i3−i3−i3i30000-111-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ672-2-22-2-222-1-222-21111-1-1-1-222-2-222-2111-1-111-1-11-1-12-20000-111-1−i3i3i3−i300001-1-11i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ682-2-22-2-222-1-222-21111-1-1-1-222-2-222-2111-1-111-1-11-1-12-20000-111-1i3−i3−i3i300001-1-11−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4000022-2-2-2-222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ714444-4-4-4-444-44-444-4-44-4-400000000-4400000000-4400000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-24-44-4-2-222-222000000002-22323−23−23−23−2323232-200000000000000000000000000000000000000000000000000
χ734444-4-4-4-4-24-44-4-2-222-222000000002-2−23−2323232323−23−232-200000000000000000000000000000000000000000000000000
χ7444-4-44-44-4400004-44-4-44-4000000000000000000000000000000000000000000000000000000004-4000000000000
χ7544-4-44-44-4400004-44-4-44-400000000000000000000000000000000000000000000000000000000-44000000000000
χ7644-4-4-44-44400004-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000022−2200
χ7744-4-4-44-44400004-4-44-4-44000000000000000000000000000000000000000000000000000000000000000000−222200
χ784-44-44-4-4440000-444-4-4-44000000000000000000000000000000000000000000000000000000000000000022−220000
χ794-44-44-4-4440000-444-4-4-440000000000000000000000000000000000000000000000000000000000000000−22220000
χ804-44-4-444-440000-44-44-44-40000000000000000000000000000000000000000000000000000004-400000000000000
χ814-44-4-444-440000-44-44-44-4000000000000000000000000000000000000000000000000000000-4400000000000000
χ824-4-4444-4-44-4-444-4-4444-4-4000000004-400000000-4400000000000000000000000000000000000000000000000000
χ834-4-4444-4-4-2-4-44422-2-2-22200000000-2223−2323−23−2323−23232-200000000000000000000000000000000000000000000000000
χ844-4-4444-4-4-2-4-44422-2-2-22200000000-22−2323−232323−2323−232-200000000000000000000000000000000000000000000000000
χ854-4-44-4-444-24-4-442222-2-2-24-44-40000-2-2-222-22-2-222200000000000000000000000000000000000000000000000000
χ864-4-44-4-444-24-4-442222-2-2-2-44-440000-2-22-2-22-222-22200000000000000000000000000000000000000000000000000
χ8788-8-88-88-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-88-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-88-8-88-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-888-8-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000000000

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