Finite Group Databasebeta

← Group #10829294

Character table — Group #10829294

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212242424242424242424244848
order122222223444466666664444444412121212121212121212121244444488881212121212121212121212121212121224242424242424242222444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-11-1
χ1011111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-1-111-11
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1-11111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1111-1-1-1-1111-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-200000000000000000000000000000000002222-2-20000000000
χ18222222222-2-2-2-2222222222-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000000000-2-2-2-2220000000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-22222-2-2-2-2000000000000000000000000000000000022-2-2-220000000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-22222-2-2-2-20000000000000000000000000000000000-2-2222-20000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-21111-1-1-1-11111-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-122-2-2-2-222-2-2-1-1-1-1-1-1-1-111111111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-12222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1-2-2222222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ29222-2-2-22-22-22-2222-2-2-2-2200002i2i−2i−2i000000002-22-22i−2i00002-2002i2i−2i−2i2i2i−2i−2i0000000022-2-200000000000000000000
χ30222-2-2-22-22-22-2222-2-2-2-2200002i2i−2i−2i000000002-22-2−2i2i0000-22002i2i−2i−2i−2i−2i2i2i00000000-2-22200000000000000000000
χ31222-2-2-22-22-22-2222-2-2-2-220000−2i−2i2i2i000000002-22-22i−2i0000-2200−2i−2i2i2i2i2i−2i−2i00000000-2-22200000000000000000000
χ32222-2-2-22-22-22-2222-2-2-2-220000−2i−2i2i2i000000002-22-2−2i2i00002-200−2i−2i2i2i−2i−2i2i2i0000000022-2-200000000000000000000
χ33222-2-2-22-2-1-22-22-1-11111-100002i2i−2i−2i33−3−333−3−3-11-112i−2i00002-200−i−iii−i−iii−i3−i3i3i3−i3−i3i3i3-1-11133−3−30000000000000000
χ34222-2-2-22-2-1-22-22-1-11111-100002i2i−2i−2i33−3−333−3−3-11-11−2i2i0000-2200−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i311-1-1−3−3330000000000000000
χ35222-2-2-22-2-1-22-22-1-11111-100002i2i−2i−2i−3−333−3−333-11-112i−2i00002-200−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3-1-111−3−3330000000000000000
χ36222-2-2-22-2-1-22-22-1-11111-100002i2i−2i−2i−3−333−3−333-11-11−2i2i0000-2200−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i311-1-133−3−30000000000000000
χ37222-2-2-22-2-1-22-22-1-11111-10000−2i−2i2i2i33−3−333−3−3-11-112i−2i0000-2200ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i311-1-1−3−3330000000000000000
χ38222-2-2-22-2-1-22-22-1-11111-10000−2i−2i2i2i33−3−333−3−3-11-11−2i2i00002-200ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i3-1-11133−3−30000000000000000
χ39222-2-2-22-2-1-22-22-1-11111-10000−2i−2i2i2i−3−333−3−333-11-112i−2i0000-2200ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i311-1-133−3−30000000000000000
χ40222-2-2-22-2-1-22-22-1-11111-10000−2i−2i2i2i−3−333−3−333-11-11−2i2i00002-200ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3-1-111−3−3330000000000000000
χ412-2-22-2-22222-2-22-2-2-2-22222-22-200002-22-22-22-222-2-200000000000000000000000000000000000000002-22-2000000
χ422-2-22-2-22222-2-22-2-2-2-22222-22-200002-22-22-22-222-2-20000000000000000000000000000000000000000-22-22000000
χ432-2-22-2-22222-2-22-2-2-2-2222-22-220000-22-22-22-2222-2-200000000000000000000000000000000000000002-2-22000000
χ442-2-22-2-22222-2-22-2-2-2-2222-22-220000-22-22-22-2222-2-20000000000000000000000000000000000000000-222-2000000
χ452-2-22-2-2222-222-2-2-2-2-22222-2-222-22-22-22-2-22-22-2-222002-20000002-22-200002-22-20000000000000000000000000000
χ462-2-22-2-2222-222-2-2-2-2-22222-2-22-22-222-22-2-22-22-2-22200-22000000-22-220000-22-220000000000000000000000000000
χ472-2-22-2-2222-222-2-2-2-2-2222-222-22-22-2-22-222-22-2-2-22200-220000002-22-20000-22-220000000000000000000000000000
χ482-2-22-2-2222-222-2-2-2-2-2222-222-2-22-22-22-222-22-2-2-222002-2000000-22-2200002-22-20000000000000000000000000000
χ492-2-22-2-222-1-222-21111-1-1-12-2-222-22-2-11-111-11-111-1-1002-2000000-11-11−i3i3−i3i3-11-11−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ502-2-22-2-222-1-222-21111-1-1-12-2-222-22-2-11-111-11-111-1-1002-2000000-11-11i3−i3i3−i3-11-11i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ512-2-22-2-222-1-222-21111-1-1-12-2-22-22-22-11-111-11-111-1-100-220000001-11-1−i3i3−i3i31-11-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ522-2-22-2-222-1-222-21111-1-1-12-2-22-22-22-11-111-11-111-1-100-220000001-11-1i3−i3i3−i31-11-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ532-2-22-2-222-1-222-21111-1-1-1-222-22-22-21-11-1-11-1111-1-100-22000000-11-11−i3i3−i3i31-11-1i3−i3i3−i3−i3i3−i3i3i3−i3i3−i30000000000000000
χ542-2-22-2-222-1-222-21111-1-1-1-222-22-22-21-11-1-11-1111-1-100-22000000-11-11i3−i3i3−i31-11-1−i3i3−i3i3i3−i3i3−i3−i3i3−i3i30000000000000000
χ552-2-22-2-222-1-222-21111-1-1-1-222-2-22-221-11-1-11-1111-1-1002-20000001-11-1−i3i3−i3i3-11-11i3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000000000000000
χ562-2-22-2-222-1-222-21111-1-1-1-222-2-22-221-11-1-11-1111-1-1002-20000001-11-1i3−i3i3−i3-11-11−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000000000000000
χ572-2-2-2222-2222-2-2-2-222-2-2200002i−2i−2i2i00000000-222-200002-2002i−2i2i−2i−2i2i000000002-2-2200002i−2i−2i2i0000000000000000
χ582-2-2-2222-2222-2-2-2-222-2-2200002i−2i−2i2i00000000-222-20000-2200−2i2i2i−2i−2i2i00000000-222-20000−2i2i2i−2i0000000000000000
χ592-2-2-2222-2222-2-2-2-222-2-220000−2i2i2i−2i00000000-222-200002-200−2i2i−2i2i2i−2i000000002-2-220000−2i2i2i−2i0000000000000000
χ602-2-2-2222-2222-2-2-2-222-2-220000−2i2i2i−2i00000000-222-20000-22002i−2i−2i2i2i−2i00000000-222-200002i−2i−2i2i0000000000000000
χ612-2-2-2222-2-122-2-211-1-111-100002i−2i−2i2i3−3−33−333−31-1-1100002-2002i−2i−iii−i3−3−33−i3i3i3−i3-111-1−i3i3i3−i3−iii−i0000000000000000
χ622-2-2-2222-2-122-2-211-1-111-100002i−2i−2i2i3−3−33−333−31-1-110000-2200−2i2i−iii−i−333−3−i3i3i3−i31-1-11i3−i3−i3i3i−i−ii0000000000000000
χ632-2-2-2222-2-122-2-211-1-111-100002i−2i−2i2i−333−33−3−331-1-1100002-2002i−2i−iii−i−333−3i3−i3−i3i3-111-1i3−i3−i3i3−iii−i0000000000000000
χ642-2-2-2222-2-122-2-211-1-111-100002i−2i−2i2i−333−33−3−331-1-110000-2200−2i2i−iii−i3−3−33i3−i3−i3i31-1-11−i3i3i3−i3i−i−ii0000000000000000
χ652-2-2-2222-2-122-2-211-1-111-10000−2i2i2i−2i3−3−33−333−31-1-1100002-200−2i2ii−i−ii3−3−33i3−i3−i3i3-111-1i3−i3−i3i3i−i−ii0000000000000000
χ662-2-2-2222-2-122-2-211-1-111-10000−2i2i2i−2i3−3−33−333−31-1-110000-22002i−2ii−i−ii−333−3i3−i3−i3i31-1-11−i3i3i3−i3−iii−i0000000000000000
χ672-2-2-2222-2-122-2-211-1-111-10000−2i2i2i−2i−333−33−3−331-1-1100002-200−2i2ii−i−ii−333−3−i3i3i3−i3-111-1−i3i3i3−i3i−i−ii0000000000000000
χ682-2-2-2222-2-122-2-211-1-111-10000−2i2i2i−2i−333−33−3−331-1-110000-22002i−2ii−i−ii3−3−33−i3i3i3−i31-1-11i3−i3−i3i3−iii−i0000000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44400002222-2-2-2-2222200000000000000000000000000000000000000000000000000
χ71444-4-4-44-444-44-444-4-4-4-440000000000000000-44-4400000000000000000000000000000000000000000000000000
χ72444-4-4-44-4-24-44-4-2-22222-2000000002323−23−23−23−2323232-22-200000000000000000000000000000000000000000000000000
χ73444-4-4-44-4-24-44-4-2-22222-200000000−23−2323232323−23−232-22-200000000000000000000000000000000000000000000000000
χ7444-444-4-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000004-4000000000000
χ7544-444-4-4-4400004-44-44-4-400000000000000000000000000000000000000000000000000000000-44000000000000
χ7644-4-4-44-44400004-4-44-44-4000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7744-4-4-44-44400004-4-44-44-40000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ784-444-44-4-440000-44-444-4-40000000000000000000000000000000000000000000000000000004-400000000000000
χ794-444-44-4-440000-44-444-4-4000000000000000000000000000000000000000000000000000000-4400000000000000
χ804-44-44-4-4440000-444-4-44-40000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ814-44-44-4-4440000-444-4-44-400000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ824-4-44-4-444-24-4-442222-2-2-24-44-40000-22-22-22-22-2-22200000000000000000000000000000000000000000000000000
χ834-4-44-4-444-24-4-442222-2-2-2-44-4400002-22-22-22-2-2-22200000000000000000000000000000000000000000000000000
χ844-4-4-4444-44-4-444-4-444-4-4400000000000000004-4-4400000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-2-4-44422-2-222-20000000023−23−232323−23−2323-222-200000000000000000000000000000000000000000000000000
χ864-4-4-4444-4-2-4-44422-2-222-200000000−232323−23−232323−23-222-200000000000000000000000000000000000000000000000000
χ8788-888-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-88-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-88-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-8-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000

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