Finite Group Databasebeta

← Group #10845223

Character table — Group #10845223

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order122222223444466666664444444412121212121212121212121244444488881212121212121212121212121212121224242424242424244444444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-11-1
χ1011111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-111-11
χ1111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-1-111-11
χ1211111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1-11111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1111-1-1-1-1111-1
χ17222222222-2-2-2-22222222220000-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000022-2-2-220000000000
χ18222222222-2-2-2-22222222220000-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2222-20000000000
χ19222222222-2-2-2-22222222-2-2000022-2-2-2-2-2-22222-2-200000000000000000000000000000000002222-2-20000000000
χ20222222222-2-2-2-22222222-2-2000022-2-2-2-2-2-22222-2-20000000000000000000000000000000000-2-2-2-2220000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-21111-1-11111-1-1-2-222-2-2-2-222-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-21111-1-11111-1-1-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111-1-12222-2-222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111-1-122-2-222-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ29222-2-2-2-2222-2-222-2-22-22-2002i2i−2i−2i0000002-200002-200002-22i−2i002i2i−2i−2i0000000022-2-200002i2i−2i−2i0000000000000000
χ30222-2-2-2-2222-2-222-2-22-22-2002i2i−2i−2i0000002-200002-20000-22−2i2i002i2i−2i−2i00000000-2-2220000−2i−2i2i2i0000000000000000
χ31222-2-2-2-2222-2-222-2-22-22-200−2i−2i2i2i0000002-200002-200002-2−2i2i00−2i−2i2i2i0000000022-2-20000−2i−2i2i2i0000000000000000
χ32222-2-2-2-2222-2-222-2-22-22-200−2i−2i2i2i0000002-200002-20000-222i−2i00−2i−2i2i2i00000000-2-22200002i2i−2i−2i0000000000000000
χ33222-2-2-2-22-12-2-22-111-11-11002i2i−2i−2i0033−3−3-1133−3−3-1100002-22i−2i00−i−iii−i3−i3i3i333−3−3-1-111−i3−i3i3i3−i−iii0000000000000000
χ34222-2-2-2-22-12-2-22-111-11-11002i2i−2i−2i0033−3−3-1133−3−3-110000-22−2i2i00−i−iii−i3−i3i3i3−3−33311-1-1i3i3−i3−i3ii−i−i0000000000000000
χ35222-2-2-2-22-12-2-22-111-11-11002i2i−2i−2i00−3−333-11−3−333-1100002-22i−2i00−i−iiii3i3−i3−i3−3−333-1-111i3i3−i3−i3−i−iii0000000000000000
χ36222-2-2-2-22-12-2-22-111-11-11002i2i−2i−2i00−3−333-11−3−333-110000-22−2i2i00−i−iiii3i3−i3−i333−3−311-1-1−i3−i3i3i3ii−i−i0000000000000000
χ37222-2-2-2-22-12-2-22-111-11-1100−2i−2i2i2i0033−3−3-1133−3−3-1100002-2−2i2i00ii−i−ii3i3−i3−i333−3−3-1-111i3i3−i3−i3ii−i−i0000000000000000
χ38222-2-2-2-22-12-2-22-111-11-1100−2i−2i2i2i0033−3−3-1133−3−3-110000-222i−2i00ii−i−ii3i3−i3−i3−3−33311-1-1−i3−i3i3i3−i−iii0000000000000000
χ39222-2-2-2-22-12-2-22-111-11-1100−2i−2i2i2i00−3−333-11−3−333-1100002-2−2i2i00ii−i−i−i3−i3i3i3−3−333-1-111−i3−i3i3i3ii−i−i0000000000000000
χ40222-2-2-2-22-12-2-22-111-11-1100−2i−2i2i2i00−3−333-11−3−333-110000-222i−2i00ii−i−i−i3−i3i3i333−3−311-1-1i3i3−i3−i3−i−iii0000000000000000
χ412-2-22-22-2222-22-2-22-2-222-2002-22-20000002-20000-22002i−2i00002i−2i2-22-200002i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ422-2-22-22-2222-22-2-22-2-222-2002-22-20000002-20000-2200−2i2i0000−2i2i2-22-20000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ432-2-22-22-2222-22-2-22-2-222-200-22-220000002-20000-22002i−2i0000−2i2i-22-2200002i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ442-2-22-22-2222-22-2-22-2-222-200-22-220000002-20000-2200−2i2i00002i−2i-22-220000−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ452-2-22-22-22-12-22-21-111-1-11002-22-2003−33−3-113−33−31-1002i−2i00002i−2i-11-113−33−3−ii−ii−i3i3−i3i3−ii−ii−i3i3−i3i30000000000000000
χ462-2-22-22-22-12-22-21-111-1-11002-22-2003−33−3-113−33−31-100−2i2i0000−2i2i-11-113−33−3i−ii−ii3−i3i3−i3i−ii−ii3−i3i3−i30000000000000000
χ472-2-22-22-22-12-22-21-111-1-11002-22-200−33−33-11−33−331-1002i−2i00002i−2i-11-11−33−33−ii−iii3−i3i3−i3−ii−iii3−i3i3−i30000000000000000
χ482-2-22-22-22-12-22-21-111-1-11002-22-200−33−33-11−33−331-100−2i2i0000−2i2i-11-11−33−33i−ii−i−i3i3−i3i3i−ii−i−i3i3−i3i30000000000000000
χ492-2-22-22-22-12-22-21-111-1-1100-22-22003−33−3-113−33−31-1002i−2i0000−2i2i1-11-1−33−33−ii−ii−i3i3−i3i3i−ii−ii3−i3i3−i30000000000000000
χ502-2-22-22-22-12-22-21-111-1-1100-22-22003−33−3-113−33−31-100−2i2i00002i−2i1-11-1−33−33i−ii−ii3−i3i3−i3−ii−ii−i3i3−i3i30000000000000000
χ512-2-22-22-22-12-22-21-111-1-1100-22-2200−33−33-11−33−331-1002i−2i0000−2i2i1-11-13−33−3−ii−iii3−i3i3−i3i−ii−i−i3i3−i3i30000000000000000
χ522-2-22-22-22-12-22-21-111-1-1100-22-2200−33−33-11−33−331-100−2i2i00002i−2i1-11-13−33−3i−ii−i−i3i3−i3i3−ii−iii3−i3i3−i30000000000000000
χ532-2-2-22-222222-2-2-2-22-2-2222-22i−2i−2i2i2-22-2-22222-2-22-2-22i−2i000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ542-2-2-22-222222-2-2-2-22-2-2222-2−2i2i2i−2i2-22-2-22222-2-22-2-2−2i2i00000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ552-2-2-22-222222-2-2-2-22-2-222-222i−2i−2i2i-22-222-222-222-2-2-2−2i2i000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ562-2-2-22-222222-2-2-2-22-2-222-22−2i2i2i−2i-22-222-222-222-2-2-22i−2i00000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ572-2-2-22-2222-2-222-2-22-2-2222-20000-222-2-22-2-2-222-22200000000000000000000000000000000000000002-22-2000000
χ582-2-2-22-2222-2-222-2-22-2-2222-20000-222-2-22-2-2-222-2220000000000000000000000000000000000000000-22-22000000
χ592-2-2-22-2222-2-222-2-22-2-222-2200002-2-222-2-2-22-2-222200000000000000000000000000000000000000002-2-22000000
χ602-2-2-22-2222-2-222-2-22-2-222-2200002-2-222-2-2-22-2-22220000000000000000000000000000000000000000-222-2000000
χ612-2-2-22-222-122-2-211-111-1-12-22i−2i−2i2i2-2-111-1-1-1-111-1112i−2i00000000−iii−ii−i−ii−i3i3i3−i3−i3i3i3−i3−333−33−3−330000000000000000
χ622-2-2-22-222-122-2-211-111-1-12-22i−2i−2i2i2-2-111-1-1-1-111-1112i−2i00000000−iii−ii−i−iii3−i3−i3i3i3−i3−i3i33−3−33−333−30000000000000000
χ632-2-2-22-222-122-2-211-111-1-12-2−2i2i2i−2i2-2-111-1-1-1-111-111−2i2i00000000i−i−ii−iii−i−i3i3i3−i3−i3i3i3−i33−3−33−333−30000000000000000
χ642-2-2-22-222-122-2-211-111-1-12-2−2i2i2i−2i2-2-111-1-1-1-111-111−2i2i00000000i−i−ii−iii−ii3−i3−i3i3i3−i3−i3i3−333−33−3−330000000000000000
χ652-2-2-22-222-122-2-211-111-1-1-222i−2i−2i2i-221-1-11-1-11-1-1111−2i2i00000000−iii−i−iii−i−i3i3i3−i3i3−i3−i3i3−333−3−333−30000000000000000
χ662-2-2-22-222-122-2-211-111-1-1-222i−2i−2i2i-221-1-11-1-11-1-1111−2i2i00000000−iii−i−iii−ii3−i3−i3i3−i3i3i3−i33−3−333−3−330000000000000000
χ672-2-2-22-222-122-2-211-111-1-1-22−2i2i2i−2i-221-1-11-1-11-1-11112i−2i00000000i−i−iii−i−ii−i3i3i3−i3i3−i3−i3i33−3−333−3−330000000000000000
χ682-2-2-22-222-122-2-211-111-1-1-22−2i2i2i−2i-221-1-11-1-11-1-11112i−2i00000000i−i−iii−i−iii3−i3−i3i3−i3i3i3−i3−333−3−333−30000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2440000-4-4-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000044222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ71444-4-4-4-444-444-44-4-44-44-4000000000000-440000-4400000000000000000000000000000000000000000000000000
χ72444-4-4-4-44-2-444-4-222-22-22000000002323−23−232-2−23−2323232-200000000000000000000000000000000000000000000000000
χ73444-4-4-4-44-2-444-4-222-22-2200000000−23−2323232-22323−23−232-200000000000000000000000000000000000000000000000000
χ7444-44-4-44-44000044-4-4-4-44000000000000000000000000000000000000000000000000000000004-4000000000000
χ7544-44-4-44-44000044-4-4-4-4400000000000000000000000000000000000000000000000000000000-44000000000000
χ7644-4-444-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000000000000022−220000
χ7744-4-444-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000000−22220000
χ784-4444-4-4-440000-4444-4-4-400000000000000000000000000000000000000000000000000000000000000000022−2200
χ794-4444-4-4-440000-4444-4-4-4000000000000000000000000000000000000000000000000000000000000000000−222200
χ804-44-4-444-440000-4-4-444-440000000000000000000000000000000000000000000000000000004i−4i00000000000000
χ814-44-4-444-440000-4-4-444-44000000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ824-4-44-44-444-44-44-44-4-444-4000000000000-4400004-400000000000000000000000000000000000000000000000000
χ834-4-44-44-44-2-44-442-222-2-220000000023−2323−232-2−2323−2323-2200000000000000000000000000000000000000000000000000
χ844-4-44-44-44-2-44-442-222-2-2200000000−2323−23232-223−2323−23-2200000000000000000000000000000000000000000000000000
χ854-4-4-44-444-2-4-44422-222-2-24-40000-44-222-2222-2-22-2-200000000000000000000000000000000000000000000000000
χ864-4-4-44-444-2-4-44422-222-2-2-4400004-42-2-2222-222-2-2-200000000000000000000000000000000000000000000000000
χ8788-88-8-88-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-888-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ898-8888-8-8-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-888-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000

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