Finite Group Databasebeta

← Group #10828724

Character table — Group #10828724

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888888888888888882424242424242424242424244848
order12222222344446666666244444466661212121212121212444444888812121212121212121212121212121212242424242424242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-111-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-111
χ6111111111111111111111-1-111-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1
χ7111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-11111-1-1
χ8111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111-1-1-1-111
χ91111-1-11111111-1-1-1-1111-111-1-11111-1-1111-1-1-1-11-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1-1-11111-1-11-1
χ101111-1-11111111-1-1-1-1111-111-1-11111-1-1111-1-1-1-11-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1111-1-1-1-111-11
χ111111-1-11111111-1-1-1-1111-111-1-11111-1-1111-1-1-1-11-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1-1-111-1-111-11
χ121111-1-11111111-1-1-1-1111-111-1-11111-1-1111-1-1-1-11-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1111-1-111-1-11-1
χ131111-1-11111111-1-1-1-1111-1-1-1-1-1-1-111-1-1111-1-1-1-111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-111111-1111-1-1-1-1-1111-1
χ141111-1-11111111-1-1-1-1111-1-1-1-1-1-1-111-1-1111-1-1-1-111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-111111-1-1-11
χ151111-1-11111111-1-1-1-1111-1-1-1-1-1-1-111-1-1111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11-1111-1-1-111-1-1-11
χ161111-1-11111111-1-1-1-1111-1-1-1-1-1-1-111-1-1111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-11-1-1-1111-1-1111-1
χ17222222222-2-2-2-22222222200-2-2002222-2-2-2-2-2-2-2-200000000000000000000000000000000000002-202-2000000
χ18222222222-2-2-2-22222222200-2-2002222-2-2-2-2-2-2-2-20000000000000000000000000000000000000-220-22000000
χ1922222222-12222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2022222222-12222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000
χ2122222222-12222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000
χ2222222222-12222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000
χ23222222-2-2222-2-22222222-2222-2-2-2-2-2-2-22-2-222-2-222-2000000002222-2-2-2-2000000000000000000000000000000
χ24222222-2-2222-2-22222222-2-2-22-222-2-2-2-22-2-222-2-22-2200000000-2-2-2-22222000000000000000000000000000000
χ25222222-2-22-2-2222222222-200-2200-2-2-2-2-222-2-222-2000000000000000000000000000000000022-200-200000000
χ26222222-2-22-2-2222222222-200-2200-2-2-2-2-222-2-222-20000000000000000000000000000000000-2-2200200000000
χ27222222-2-2-122-2-2-1-1-1-1-1-1-1-2222-2-2-21111-111-1-111-12-200000000-1-1-1-11111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000
χ28222222-2-2-122-2-2-1-1-1-1-1-1-1-2222-2-2-21111-111-1-111-12-200000000-1-1-1-11111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000
χ29222222-2-2-122-2-2-1-1-1-1-1-1-1-2-2-22-2221111-111-1-111-1-22000000001111-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000
χ30222222-2-2-122-2-2-1-1-1-1-1-1-1-2-2-22-2221111-111-1-111-1-22000000001111-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000
χ312222-2-2222-2-2-2-2-2-2-2-2222-200220022-2-2-2-2-22222-200000000000000000000000000000000000002-20-22000000
χ322222-2-2222-2-2-2-2-2-2-2-2222-200220022-2-2-2-2-22222-20000000000000000000000000000000000000-2202-2000000
χ332222-2-222-122221111-1-1-1-222-2-222-1-111-1-1-11111-1-2-222-2-222-2-2-1-111-1-111-1-1-1-11111-1-1-1-1111100000000000000
χ342222-2-222-122221111-1-1-1-222-2-222-1-111-1-1-11111-1-2-2-2-222-2-222-1-111-1-1111111-1-1-1-11111-1-1-1-100000000000000
χ352222-2-222-122221111-1-1-1-2-2-2-2-2-2-2-1-111-1-1-11111-12222-2-2-2-22211-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000
χ362222-2-222-122221111-1-1-1-2-2-2-2-2-2-2-1-111-1-1-11111-122-2-22222-2-211-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000
χ372222-2-2-2-2222-2-2-2-2-2-2222222-22-2-2-2-2222-2-2-2-2222-220000000022-2-2-2-222000000000000000000000000000000
χ382222-2-2-2-2222-2-2-2-2-2-22222-2-2-2222-2-2222-2-2-2-22222-200000000-2-22222-2-2000000000000000000000000000000
χ392222-2-2-2-22-2-222-2-2-2-22222002-200-2-222-22222-2-2-200000000000000000000000000000000002-2-200200000000
χ402222-2-2-2-22-2-222-2-2-2-22222002-200-2-222-22222-2-2-20000000000000000000000000000000000-22200-200000000
χ412222-2-2-2-2-122-2-21111-1-1-1222-22-2-211-1-1-11111-1-1-1-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000
χ422222-2-2-2-2-122-2-21111-1-1-1222-22-2-211-1-1-11111-1-1-1-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000
χ432222-2-2-2-2-122-2-21111-1-1-12-2-2-222211-1-1-11111-1-1-12-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000
χ442222-2-2-2-2-122-2-21111-1-1-12-2-2-222211-1-1-11111-1-1-12-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000
χ452-22-2002-22-222-200002-2-202i−2i002i−2i2-200-22-20000200002i−2i002-22i−2i002i−2i0000002i−2i2i−2i00002-22-200000000000000
χ462-22-2002-22-222-200002-2-202i−2i002i−2i2-200-22-2000020000−2i2i00-222i−2i002i−2i000000−2i2i−2i2i0000-22-2200000000000000
χ472-22-2002-22-222-200002-2-20−2i2i00−2i2i2-200-22-20000200002i−2i00-22−2i2i00−2i2i0000002i−2i2i−2i0000-22-2200000000000000
χ482-22-2002-22-222-200002-2-20−2i2i00−2i2i2-200-22-2000020000−2i2i002-2−2i2i00−2i2i000000−2i2i−2i2i00002-22-200000000000000
χ492-22-2002-2-1-222-2−i3−i3i3i3-11102i−2i002i−2i-11−i3i31-11−i3i3−i3i3-100002i−2i002-2−ii3−3−ii3−33−33−3−ii−ii−i3i3−i3i3-11-1100000000000000
χ502-22-2002-2-1-222-2−i3−i3i3i3-11102i−2i002i−2i-11−i3i31-11−i3i3−i3i3-10000−2i2i00-22−ii3−3−ii3−3−33−33i−ii−ii3−i3i3−i31-11-100000000000000
χ512-22-2002-2-1-222-2−i3−i3i3i3-1110−2i2i00−2i2i-11−i3i31-11−i3i3−i3i3-100002i−2i00-22i−i−33i−i−333−33−3−ii−iii3−i3i3−i31-11-100000000000000
χ522-22-2002-2-1-222-2−i3−i3i3i3-1110−2i2i00−2i2i-11−i3i31-11−i3i3−i3i3-10000−2i2i002-2i−i−33i−i−33−33−33i−ii−i−i3i3−i3i3-11-1100000000000000
χ532-22-2002-2-1-222-2i3i3−i3−i3-11102i−2i002i−2i-11i3−i31-11i3−i3i3−i3-100002i−2i002-2−ii−33−ii−33−33−33−ii−iii3−i3i3−i3-11-1100000000000000
χ542-22-2002-2-1-222-2i3i3−i3−i3-11102i−2i002i−2i-11i3−i31-11i3−i3i3−i3-10000−2i2i00-22−ii−33−ii−333−33−3i−ii−i−i3i3−i3i31-11-100000000000000
χ552-22-2002-2-1-222-2i3i3−i3−i3-1110−2i2i00−2i2i-11i3−i31-11i3−i3i3−i3-100002i−2i00-22i−i3−3i−i3−3−33−33−ii−ii−i3i3−i3i31-11-100000000000000
χ562-22-2002-2-1-222-2i3i3−i3−i3-1110−2i2i00−2i2i-11i3−i31-11i3−i3i3−i3-10000−2i2i002-2i−i3−3i−i3−33−33−3i−ii−ii3−i3i3−i3-11-1100000000000000
χ572-22-200-222-22-2200002-2-202i−2i00−2i2i-2200-2-2200002002i−2i002-2002i−2i00−2i2i002i−2i−2i2i00002-2-22000000000000000000
χ582-22-200-222-22-2200002-2-202i−2i00−2i2i-2200-2-220000200−2i2i00-22002i−2i00−2i2i00−2i2i2i−2i0000-222-2000000000000000000
χ592-22-200-222-22-2200002-2-20−2i2i002i−2i-2200-2-2200002002i−2i00-2200−2i2i002i−2i002i−2i−2i2i0000-222-2000000000000000000
χ602-22-200-222-22-2200002-2-20−2i2i002i−2i-2200-2-220000200−2i2i002-200−2i2i002i−2i00−2i2i2i−2i00002-2-22000000000000000000
χ612-22-200-22-1-22-22−i3−i3i3i3-11102i−2i00−2i2i1-1i3−i311-1−i3i3i3−i3-1002i−2i002-200−ii3−3i−i−33−iii−i3−3−33-111-1−i3i3i3−i300000000000000
χ622-22-200-22-1-22-22−i3−i3i3i3-11102i−2i00−2i2i1-1i3−i311-1−i3i3i3−i3-100−2i2i00-2200−ii3−3i−i−33i−i−ii−333−31-1-11i3−i3−i3i300000000000000
χ632-22-200-22-1-22-22−i3−i3i3i3-1110−2i2i002i−2i1-1i3−i311-1−i3i3i3−i3-1002i−2i00-2200i−i−33−ii3−3−iii−i3−3−331-1-11i3−i3−i3i300000000000000
χ642-22-200-22-1-22-22−i3−i3i3i3-1110−2i2i002i−2i1-1i3−i311-1−i3i3i3−i3-100−2i2i002-200i−i−33−ii3−3i−i−ii−333−3-111-1−i3i3i3−i300000000000000
χ652-22-200-22-1-22-22i3i3−i3−i3-11102i−2i00−2i2i1-1−i3i311-1i3−i3−i3i3-1002i−2i002-200−ii−33i−i3−3−iii−i−333−3-111-1i3−i3−i3i300000000000000
χ662-22-200-22-1-22-22i3i3−i3−i3-11102i−2i00−2i2i1-1−i3i311-1i3−i3−i3i3-100−2i2i00-2200−ii−33i−i3−3i−i−ii3−3−331-1-11−i3i3i3−i300000000000000
χ672-22-200-22-1-22-22i3i3−i3−i3-1110−2i2i002i−2i1-1−i3i311-1i3−i3−i3i3-1002i−2i00-2200i−i3−3−ii−33−iii−i−333−31-1-11−i3i3i3−i300000000000000
χ682-22-200-22-1-22-22i3i3−i3−i3-1110−2i2i002i−2i1-1−i3i311-1i3−i3−i3i3-100−2i2i002-200i−i3−3−ii−33i−i−ii3−3−33-111-1i3−i3−i3i300000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2400-4-400-2-2-2-222222222000000000000000000000000000000000000000000000000
χ70444444-4-4-2-4-444-2-2-2-2-2-2-2-400-440022222-2-222-2-22000000000000000000000000000000000000000000000000
χ714444-4-444-2-4-4-4-42222-2-2-2-4004400-2-222222-2-2-2-22000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-2-4-4442222-2-2-24004-40022-2-22-2-2-2-2222000000000000000000000000000000000000000000000000
χ7344-4-44-400400004-44-4-44-400000000000000000000000000000000000000000000000000000000000002-22-200
χ7444-4-44-400400004-44-4-44-40000000000000000000000000000000000000000000000000000000000000-22-2200
χ7544-4-4-440040000-44-44-44-400000000000000000000000000000000000000000000000000000000000002-2-2200
χ7644-4-4-440040000-44-44-44-40000000000000000000000000000000000000000000000000000000000000-222-200
χ774-44-4004-444-4-4400004-4-400000004-4004-440000-4000000000000000000000000000000000000000000000000
χ784-44-4004-4-24-4-44−2i3−2i32i32i3-2220000000-22−2i32i3-22-22i3−2i32i3−2i32000000000000000000000000000000000000000000000000
χ794-44-4004-4-24-4-442i32i3−2i3−2i3-2220000000-222i3−2i3-22-2−2i32i3−2i32i32000000000000000000000000000000000000000000000000
χ804-44-400-4444-44-400004-4-40000000-440044-40000-4000000000000000000000000000000000000000000000000
χ814-44-400-44-24-44-4−2i3−2i32i32i3-22200000002-22i3−2i3-2-222i3−2i3−2i32i32000000000000000000000000000000000000000000000000
χ824-44-400-44-24-44-42i32i3−2i3−2i3-22200000002-2−2i32i3-2-22−2i32i32i3−2i32000000000000000000000000000000000000000000000000
χ8388-8-88-800-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8800-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000000
χ858-8-880000800000000-8-880000000000000000000000000000000000000000000000000000000000000000000
χ868-8-880000-40000−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000000000
χ878-8-880000-400004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000000000

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