Finite Group Databasebeta

← Group #10831722

Character table — Group #10831722

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666664444444444441212121212121212121212121212121212121212121212124444444412121212121212121212121212121212121222448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11-1
χ6111111111111111111111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-11
χ7111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-11
χ8111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-11-1
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-1111111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-2-2-200000000222222222222-200-20000-2-20000-2-20000-2-2000000000000000000
χ18222222222-2-2-2-22222222000022-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-2222220020000-2-2000022000022000000000000000000
χ19222222222-2-2-2-222222220000-2-22222-2-2-2-2-2-2000000002222-2-2-2-2-2-2-2-2-20020000220000-2-2000022000000000000000000
χ20222222222-2-2-2-222222220000-2-222-2-222-2-2-2-200000000-2-2-2-22222-2-2-2-2200-20000220000220000-2-2000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-2-2-2-2-2-222-1-1-1-1-1-111111111111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111222-2-2-2-2-2111111-1-1-1-1-1-111111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-2-2-2222-2-2111111111111-1-1-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222222222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-2-2-2-1-11111-1-11111-1-1111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-222-222-2-2-1-1111111-1-1-1-111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-1-1-1-111111111-1-1-1-1111111112-2-2-2222211-1-1-1-1-1-1111111-1-1-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-222-1-1-1-1111111111111-1-1-1-11111-2222-2-22211-1-1-1-111-1-1-1-1-1-1111100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-222221111−i3−i3−i3−i3i3i3i3i3-1-1-1-1-1-1-1-1-1-1-1-1-200-2000011−i3−i3i3i311−i3−i3i3i311−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-222221111i3i3i3i3−i3−i3−i3−i3-1-1-1-1-1-1-1-1-1-1-1-1-200-2000011i3i3−i3−i311i3i3−i3−i311i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-2-2-2-2-21111−i3−i3−i3−i3i3i3i3i311111111-1-1-1-12002000011−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-2-2-2-2-21111i3i3i3i3−i3−i3−i3−i311111111-1-1-1-12002000011i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-22222-2-21111−i3−i3−i3−i3i3i3i3i3-1-1-1-111111111-20020000-1-1i3i3−i3−i311−i3−i3i3i3-1-1i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-22222-2-21111i3i3i3i3−i3−i3−i3−i3-1-1-1-111111111-20020000-1-1−i3−i3i3i311i3i3−i3−i3-1-1−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-222-2-2221111−i3−i3−i3−i3i3i3i3i31111-1-1-1-11111200-20000-1-1i3i3−i3−i3-1-1i3i3−i3−i311−i3−i3i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-222-2-2221111i3i3i3i3−i3−i3−i3−i31111-1-1-1-11111200-20000-1-1−i3−i3i3i3-1-1−i3−i3i3i311i3i3−i3−i300000000000000
χ372222-2-2-2-2222-2-222-2-22-2-222-2-20000000022-2-222-2-222-2-2000000000000000000000000000000000000002-2002-200000000
χ382222-2-2-2-2222-2-222-2-22-2-222-2-20000000022-2-222-2-222-2-200000000000000000000000000000000000000-2200-2200000000
χ392222-2-2-2-2222-2-222-2-22-2-2-2-2220000000022-2-2-2-222-2-222000000000000000000000000000000000000002-200-2200000000
χ402222-2-2-2-2222-2-222-2-22-2-2-2-2220000000022-2-2-2-222-2-22200000000000000000000000000000000000000-22002-200000000
χ412-2-2222-2-22-22-22-2-2222-2-22-22-2000000002-22-22-22-22-22-200000000000000000000000000000000000000002i−2i002i−2i000000
χ422-2-2222-2-22-22-22-2-2222-2-22-22-2000000002-22-22-22-22-22-20000000000000000000000000000000000000000−2i2i00−2i2i000000
χ432-2-2222-2-22-22-22-2-2222-2-2-22-22000000002-22-2-22-22-22-2200000000000000000000000000000000000000002i−2i00−2i2i000000
χ442-2-2222-2-22-22-22-2-2222-2-2-22-22000000002-22-2-22-22-22-220000000000000000000000000000000000000000−2i2i002i−2i000000
χ452-2-22-2-22222-2-22-2-2-2-222200002-22-20000-222-2000000000000000022-2-202-202-2002-20000002-22-2002-22-200000000000000
χ462-2-22-2-22222-2-22-2-2-2-222200002-22-20000-222-2000000000000000022-2-20-220-22002-2000000-22-2200-22-2200000000000000
χ472-2-22-2-22222-2-22-2-2-2-22220000-22-220000-222-20000000000000000-2-22202-20-2200-220000002-22-200-22-2200000000000000
χ482-2-22-2-22222-2-22-2-2-2-22220000-22-220000-222-20000000000000000-2-2220-2202-200-22000000-22-22002-22-200000000000000
χ492-2-22-2-2222-222-2-2-2-2-22222-2-222-2-2200002-2-222-2-222-2-220000000022-2-20000002-2-222-22-200000000000000000000000000
χ502-2-22-2-2222-222-2-2-2-2-22222-2-22-222-200002-2-222-2-222-2-2200000000-2-222000000-222-2-22-2200000000000000000000000000
χ512-2-22-2-2222-222-2-2-2-2-2222-222-22-2-2200002-2-22-222-2-222-20000000022-2-2000000-22-22-22-2200000000000000000000000000
χ522-2-22-2-2222-222-2-2-2-2-2222-222-2-222-200002-2-22-222-2-222-200000000-2-2220000002-22-22-22-200000000000000000000000000
χ532-2-22-2-222-12-2-221111-1-1-100002-22-200001-1-11−i3i3i3−i3i3−i3−i3i3−i3−i3i3i3−i3−i3i3i3-1-11102-202-200-11−i3i3i3−i3−i3i3-11-11−i3i3-11-1100000000000000
χ542-2-22-2-222-12-2-221111-1-1-100002-22-200001-1-11−i3i3i3−i3i3−i3−i3i3i3i3−i3−i3i3i3−i3−i3-1-1110-220-2200-11−i3i3i3−i3i3−i31-11-1i3−i31-11-100000000000000
χ552-2-22-2-222-12-2-221111-1-1-100002-22-200001-1-11i3−i3−i3i3−i3i3i3−i3−i3−i3i3i3−i3−i3i3i3-1-1110-220-2200-11i3−i3−i3i3−i3i31-11-1−i3i31-11-100000000000000
χ562-2-22-2-222-12-2-221111-1-1-100002-22-200001-1-11i3−i3−i3i3−i3i3i3−i3i3i3−i3−i3i3i3−i3−i3-1-11102-202-200-11i3−i3−i3i3i3−i3-11-11i3−i3-11-1100000000000000
χ572-2-22-2-222-12-2-221111-1-1-10000-22-2200001-1-11−i3i3i3−i3i3−i3−i3i3−i3−i3i3i3i3i3−i3−i311-1-102-20-22001-1i3−i3−i3i3−i3i3-11-11i3−i31-11-100000000000000
χ582-2-22-2-222-12-2-221111-1-1-10000-22-2200001-1-11−i3i3i3−i3i3−i3−i3i3i3i3−i3−i3−i3−i3i3i311-1-10-2202-2001-1i3−i3−i3i3i3−i31-11-1−i3i3-11-1100000000000000
χ592-2-22-2-222-12-2-221111-1-1-10000-22-2200001-1-11i3−i3−i3i3−i3i3i3−i3−i3−i3i3i3i3i3−i3−i311-1-10-2202-2001-1−i3i3i3−i3−i3i31-11-1i3−i3-11-1100000000000000
χ602-2-22-2-222-12-2-221111-1-1-10000-22-2200001-1-11i3−i3−i3i3−i3i3i3−i3i3i3−i3−i3−i3−i3i3i311-1-102-20-22001-1−i3i3i3−i3i3−i3-11-11−i3i31-11-100000000000000
χ612-2-22-2-222-1-222-21111-1-1-12-2-222-2-220000-111-1-111-1-111-1−i3−i3i3i3−i3−i3i3i3-1-1110000002-21-1-11-11i3−i3−i3i3i3−i3i3−i3−i3i3i3−i300000000000000
χ622-2-22-2-222-1-222-21111-1-1-12-2-222-2-220000-111-1-111-1-111-1i3i3−i3−i3i3i3−i3−i3-1-1110000002-21-1-11-11−i3i3i3−i3−i3i3−i3i3i3−i3−i3i300000000000000
χ632-2-22-2-222-1-222-21111-1-1-12-2-22-222-20000-111-1-111-1-111-1−i3−i3i3i3i3i3−i3−i311-1-1000000-22-111-11-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000
χ642-2-22-2-222-1-222-21111-1-1-12-2-22-222-20000-111-1-111-1-111-1i3i3−i3−i3−i3−i3i3i311-1-1000000-22-111-11-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000
χ652-2-22-2-222-1-222-21111-1-1-1-222-22-2-220000-111-11-1-111-1-11−i3−i3i3i3−i3−i3i3i3-1-111000000-221-11-11-1i3−i3i3−i3−i3i3i3−i3i3−i3−i3i300000000000000
χ662-2-22-2-222-1-222-21111-1-1-1-222-22-2-220000-111-11-1-111-1-11i3i3−i3−i3i3i3−i3−i3-1-111000000-221-11-11-1−i3i3−i3i3i3−i3−i3i3−i3i3i3−i300000000000000
χ672-2-22-2-222-1-222-21111-1-1-1-222-2-222-20000-111-11-1-111-1-11−i3−i3i3i3i3i3−i3−i311-1-10000002-2-11-11-11i3−i3i3−i3−i3i3−i3i3−i3i3i3−i300000000000000
χ682-2-22-2-222-1-222-21111-1-1-1-222-2-222-20000-111-11-1-111-1-11i3i3−i3−i3−i3−i3i3i311-1-10000002-2-11-11-11−i3i3−i3i3i3−i3i3−i3i3−i3−i3i300000000000000
χ694444-4-4-4-44-4-44444-4-44-4-4000000000000-4-444000000000000000000000000000000000000000000000000000000000000
χ704444-4-4-4-4-244-4-4-2-222-22244-4-400000000-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ714444-4-4-4-4-244-4-4-2-222-222-4-44400000000-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-2-4-444-2-222-22200000000000022-2-2−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000000000000000
χ734444-4-4-4-4-2-4-444-2-222-22200000000000022-2-22i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000000000000000
χ7444-4-44-44-4400004-44-4-4-4400000000004i−4i00000000000000004i−4i4i−4i00000000000000000000000000000000000000000000
χ7544-4-44-44-4400004-44-4-4-440000000000−4i4i0000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ7644-4-44-44-4-20000-22-2222-200000000004i−4i00000000000023−2323−23−2i2i−2i2i−2i32i3−2i32i30000000000000000000000000000000000000000
χ7744-4-44-44-4-20000-22-2222-200000000004i−4i000000000000−2323−2323−2i2i−2i2i2i3−2i32i3−2i30000000000000000000000000000000000000000
χ7844-4-44-44-4-20000-22-2222-20000000000−4i4i00000000000023−2323−232i−2i2i−2i2i3−2i32i3−2i30000000000000000000000000000000000000000
χ7944-4-44-44-4-20000-22-2222-20000000000−4i4i000000000000−2323−23232i−2i2i−2i−2i32i3−2i32i30000000000000000000000000000000000000000
χ8044-4-4-44-44400004-4-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ8144-4-4-44-44400004-4-44-44-40000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ824-44-44-4-4440000-444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ834-44-44-4-4440000-444-4-44-400000000000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ844-44-4-444-440000-44-44-4-44000000004i−4i000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ854-44-4-444-440000-44-44-4-4400000000−4i4i00000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ864-44-4-444-4-200002-22-222-2000000004i−4i00000000000000−2i2i2i−2i23−23−2323−2i32i32i3−2i30000000000000000000000000000000000000000
χ874-44-4-444-4-200002-22-222-2000000004i−4i00000000000000−2i2i2i−2i−232323−232i3−2i3−2i32i30000000000000000000000000000000000000000
χ884-44-4-444-4-200002-22-222-200000000−4i4i000000000000002i−2i−2i2i23−23−23232i3−2i3−2i32i30000000000000000000000000000000000000000
χ894-44-4-444-4-200002-22-222-200000000−4i4i000000000000002i−2i−2i2i−232323−23−2i32i32i3−2i30000000000000000000000000000000000000000
χ904-4-4444-4-444-44-4-4-4444-4-4000000000000-44-44000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-4-4-24-44-422-2-2-2220000000000002-22-2−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000000000000000000000000000
χ924-4-4444-4-4-24-44-422-2-2-2220000000000002-22-22i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000000000000000000000000000
χ934-4-4444-4-4-2-44-4422-2-2-2224-44-400000000-22-22-22-22-22-220000000000000000000000000000000000000000000000000000
χ944-4-4444-4-4-2-44-4422-2-2-222-44-4400000000-22-222-22-22-22-20000000000000000000000000000000000000000000000000000
χ9588-8-8-88-88-40000-444-44-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-88-8-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000000000

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