Finite Group Databasebeta

← Group #10827619

Character table — Group #10827619

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666662222444444446666121212121212121212121212121212121212121244444444661212121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ911111111111111111111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111111111111111-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1111111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ1311111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111111111-1-11-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-11
χ1411111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111111111-1-11-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111-1
χ1511111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-1111111-1-1-1-111-1-111-1-1-1-111-11
χ1611111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-11111-1-11-1
χ17222222222-2-2-2-222222222222-2-20000-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000200-200220000-2-2220000000000000000000000
χ18222222222-2-2-2-2222222222-2-2220000-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000-20020022000022-2-20000000000000000000000
χ19222222222-2-2-2-22222222-2-2222200002222222222-2-2-2-222220000000000-200-200-2-20000-2-2-2-20000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2000022-2-2-2-2-2-2-2-2-2-2-2-222220000000000200200-2-2000022220000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-22-2-22-2-2-1-11111-1-1-1-11111111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-111111111111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-2-2-222-222-1-111111111-1-1-1-1-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-22222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2222-2-2111111-1-111-1-1-1-1111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-2-2-1-1-1-11111-1-1-1-111111111111122-2-2-222211-1-1-1-1-1-1111111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-2-21111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-22-2-2-22211111111-1-11111-1-1-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-21111-1-1-1-1-1-1-1-111111111111122222-2-2-211-1-1-1-111-1-1-1-1-1-1111100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-20000-2-2-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i300200-200-1-1−i3−i3i3i311-1-1−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-20000-2-2-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i300200-200-1-1i3i3−i3−i311-1-1i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2220000-2-21111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i300-200200-1-1−i3−i3i3i3-1-111i3i3−i3−i3i3i3−i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2220000-2-21111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i300-200200-1-1i3i3−i3−i3-1-111−i3−i3i3i3−i3−i3i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222000022-1-1-1-1-1-1-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i300-200-20011i3i3−i3−i31111−i3−i3i3i3i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222000022-1-1-1-1-1-1-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i300-200-20011−i3−i3i3i31111i3i3−i3−i3−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2000022111111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i30020020011i3i3−i3−i3-1-1-1-1i3i3−i3−i3−i3−i3i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2000022111111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i30020020011−i3−i3i3i3-1-1-1-1−i3−i3i3i3i3i3−i3−i300000000000000
χ3722-2-2-22-22222-2-222-2-2-22-20000002i2i−2i−2i000000000022-2-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-20000002i−2i00
χ3822-2-2-22-22222-2-222-2-2-22-20000002i2i−2i−2i000000000022-2-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22000000−2i2i00
χ3922-2-2-22-22222-2-222-2-2-22-2000000−2i−2i2i2i000000000022-2-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-2000000−2i2i00
χ4022-2-2-22-22222-2-222-2-2-22-2000000−2i−2i2i2i000000000022-2-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-220000002i−2i00
χ412-22-2-2-22222-22-2-2-222-22-20000002i−2i2i−2i00000000002-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000002-20000002i−2i0000
χ422-22-2-2-22222-22-2-2-222-22-20000002i−2i2i−2i00000000002-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000-22000000−2i2i0000
χ432-22-2-2-22222-22-2-2-222-22-2000000−2i2i−2i2i00000000002-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000002-2000000−2i2i0000
χ442-22-2-2-22222-22-2-2-222-22-2000000−2i2i−2i2i00000000002-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000-220000002i−2i0000
χ452-2-222-2-2222-2-22-2-2-2-22222-200002-2-222-2000000002-2-2222-2-22-2-222-2-222-20000002-22-22-200000000000000000000000000
χ462-2-222-2-2222-2-22-2-2-2-22222-20000-222-22-2000000002-2-2222-2-2-222-2-222-2-220000002-2-22-2200000000000000000000000000
χ472-2-222-2-2222-2-22-2-2-2-2222-2200002-2-22-22000000002-2-22-2-2222-2-222-2-22-22000000-22-22-2200000000000000000000000000
χ482-2-222-2-2222-2-22-2-2-2-2222-220000-222-2-22000000002-2-22-2-222-222-2-222-22-2000000-222-22-200000000000000000000000000
χ492-2-222-2-222-222-2-2-2-2-22222-200000000-2200000000-222-2-2-222000000000002-202-22-2000000002-22-22-22-200000000000000
χ502-2-222-2-222-222-2-2-2-2-22222-200000000-2200000000-222-2-2-22200000000000-220-222-200000000-22-22-22-2200000000000000
χ512-2-222-2-222-222-2-2-2-2-2222-22000000002-200000000-222-222-2-2000000000002-20-22-22000000002-22-2-22-2200000000000000
χ522-2-222-2-222-222-2-2-2-2-2222-22000000002-200000000-222-222-2-200000000000-2202-2-2200000000-22-222-22-200000000000000
χ532-2-222-2-22-12-2-221111-1-1-12-200002-2-222-2−i3−i3i3i3−i3−i3i3i3-111-1-1-111-111-1-111-12-2000000-11-11-11−i3i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000
χ542-2-222-2-22-12-2-221111-1-1-12-200002-2-222-2i3i3−i3−i3i3i3−i3−i3-111-1-1-111-111-1-111-12-2000000-11-11-11i3−i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000
χ552-2-222-2-22-12-2-221111-1-1-12-20000-222-22-2−i3−i3i3i3−i3−i3i3i3-111-1-1-1111-1-111-1-11-22000000-111-11-1−i3i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000
χ562-2-222-2-22-12-2-221111-1-1-12-20000-222-22-2i3i3−i3−i3i3i3−i3−i3-111-1-1-1111-1-111-1-11-22000000-111-11-1i3−i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000
χ572-2-222-2-22-12-2-221111-1-1-1-2200002-2-22-22−i3−i3i3i3i3i3−i3−i3-111-111-1-1-111-1-111-1-220000001-11-11-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300000000000000
χ582-2-222-2-22-12-2-221111-1-1-1-2200002-2-22-22i3i3−i3−i3−i3−i3i3i3-111-111-1-1-111-1-111-1-220000001-11-11-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300000000000000
χ592-2-222-2-22-12-2-221111-1-1-1-220000-222-2-22−i3−i3i3i3i3i3−i3−i3-111-111-1-11-1-111-1-112-20000001-1-11-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300000000000000
χ602-2-222-2-22-12-2-221111-1-1-1-220000-222-2-22i3i3−i3−i3−i3−i3i3i3-111-111-1-11-1-111-1-112-20000001-1-11-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000000000
χ612-2-222-2-22-1-222-21111-1-1-12-200000000-22−i3−i3i3i3i3i3−i3−i31-1-1111-1-1−i3i3i3−i3i3−i3−i3i30002-202-2-11−i3i3i3−i3i3−i3−i3i3-11-11-11-1100000000000000
χ622-2-222-2-22-1-222-21111-1-1-12-200000000-22−i3−i3i3i3i3i3−i3−i31-1-1111-1-1i3−i3−i3i3−i3i3i3−i3000-220-22-11i3−i3−i3i3i3−i3−i3i31-11-11-11-100000000000000
χ632-2-222-2-22-1-222-21111-1-1-12-200000000-22i3i3−i3−i3−i3−i3i3i31-1-1111-1-1−i3i3i3−i3i3−i3−i3i3000-220-22-11−i3i3i3−i3−i3i3i3−i31-11-11-11-100000000000000
χ642-2-222-2-22-1-222-21111-1-1-12-200000000-22i3i3−i3−i3−i3−i3i3i31-1-1111-1-1i3−i3−i3i3−i3i3i3−i30002-202-2-11i3−i3−i3i3−i3i3i3−i3-11-11-11-1100000000000000
χ652-2-222-2-22-1-222-21111-1-1-1-22000000002-2−i3−i3i3i3−i3−i3i3i31-1-11-1-111−i3i3i3−i3i3−i3−i3i30002-20-221-1i3−i3−i3i3i3−i3i3−i3-11-111-11-100000000000000
χ662-2-222-2-22-1-222-21111-1-1-1-22000000002-2−i3−i3i3i3−i3−i3i3i31-1-11-1-111i3−i3−i3i3−i3i3i3−i3000-2202-21-1−i3i3i3−i3i3−i3i3−i31-11-1-11-1100000000000000
χ672-2-222-2-22-1-222-21111-1-1-1-22000000002-2i3i3−i3−i3i3i3−i3−i31-1-11-1-111−i3i3i3−i3i3−i3−i3i3000-2202-21-1i3−i3−i3i3−i3i3−i3i31-11-1-11-1100000000000000
χ682-2-222-2-22-1-222-21111-1-1-1-22000000002-2i3i3−i3−i3i3i3−i3−i31-1-11-1-111i3−i3−i3i3−i3i3i3−i30002-20-221-1−i3i3i3−i3−i3i3−i3i3-11-111-11-100000000000000
χ69444-44-4-4-4400004-44-4-4-44004-4000000004-44-4000000000000000000000000000000000000000000000000000000000000
χ70444-44-4-4-4400004-44-4-4-4400-4400000000-44-44000000000000000000000000000000000000000000000000000000000000
χ71444-44-4-4-4-20000-22-2222-2004-400000000-22-2223−2323−23000023−2323−23000000000000000000000000000000000000000000000000
χ72444-44-4-4-4-20000-22-2222-2004-400000000-22-22−2323−23230000−2323−2323000000000000000000000000000000000000000000000000
χ73444-44-4-4-4-20000-22-2222-200-44000000002-22-223−2323−230000−2323−2323000000000000000000000000000000000000000000000000
χ74444-44-4-4-4-20000-22-2222-200-44000000002-22-2−2323−2323000023−2323−23000000000000000000000000000000000000000000000000
χ7544-44-4-44-4400004-4-444-4-40000000000000000000000000000000000000000000000000000000000000000000022−22000000
χ7644-44-4-44-4400004-4-444-4-400000000000000000000000000000000000000000000000000000000000000000000−2222000000
χ7744-4-4-44-444-4-44444-4-4-44-400000000000000000000-4-4440000000000000000000000000000000000000000000000000000
χ7844-4-4-44-44-244-4-4-2-2222-220000004i4i−4i−4i0000000000-2-2220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ7944-4-4-44-44-244-4-4-2-2222-22000000−4i−4i4i4i0000000000-2-22200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ8044-4-4-44-44-2-4-444-2-2222-220000000000000000000022-2-200002323−23−23−23−2323230000000000000000000000000000000000000000
χ8144-4-4-44-44-2-4-444-2-2222-220000000000000000000022-2-20000−23−2323232323−23−230000000000000000000000000000000000000000
χ824-444-44-4-440000-444-44-4-400000000000000000000000000000000000000000000000000000000000000000022−2200000000
χ834-444-44-4-440000-444-44-4-4000000000000000000000000000000000000000000000000000000000000000000−222200000000
χ844-44-4-4-4444-44-44-4-444-44-400000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ854-44-4-4-444-24-44-422-2-22-220000004i−4i4i−4i0000000000-22-220000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ864-44-4-4-444-24-44-422-2-22-22000000−4i4i−4i4i0000000000-22-2200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ874-44-4-4-444-2-44-4422-2-22-22000000000000000000002-22-2000023−2323−23−2323−23230000000000000000000000000000000000000000
χ884-44-4-4-444-2-44-4422-2-22-22000000000000000000002-22-20000−2323−232323−2323−230000000000000000000000000000000000000000
χ894-4-4-4444-440000-44-44-4-4400004i−4i00000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ904-4-4-4444-440000-44-44-4-440000−4i4i0000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ914-4-4-4444-4-200002-22-222-200004i−4i000000−2i32i32i3−2i3−2i2i2i−2i000023−23−2323000000000000000000000000000000000000000000000000
χ924-4-4-4444-4-200002-22-222-200004i−4i0000002i3−2i3−2i32i3−2i2i2i−2i0000−232323−23000000000000000000000000000000000000000000000000
χ934-4-4-4444-4-200002-22-222-20000−4i4i000000−2i32i32i3−2i32i−2i−2i2i0000−232323−23000000000000000000000000000000000000000000000000
χ944-4-4-4444-4-200002-22-222-20000−4i4i0000002i3−2i3−2i32i32i−2i−2i2i000023−23−2323000000000000000000000000000000000000000000000000
χ9588-88-8-88-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-88-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000000000000000

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