Finite Group Databasebeta

← Group #10848609

Character table — Group #10848609

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888881212121212121212161616161616161616161616242424242424242424242424
order122222344444444666444444661212121212121212246612121212121212124444444444881212121224242424222244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ711111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111
χ811111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-11-11-1-111-1-111-1-111-1-11111-1-1
χ1111111111-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111-11-111-1-111-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11-1-111-1-11111-1-111-1-1-1-111
χ1311111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-111-1-111
χ1411111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-111
χ1511111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-111-1-1
χ1611111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-111-1-1-11111-1-111-1-1-1-11111-1-1
χ172222222-222-2-2-2-2-22222-200002222-2-2-2-2-2-200002-2000000000000000000000000002-22-200000000
χ182222222-222-2-2-2-2-22222-200002222-2-2-2-2-2-200002-200000000000000000000000000-22-2200000000
χ192222222-2-2-222-2-2-2222-22000022-2-222-2-2-2-20000-22000000000000000000000000002-2-2200000000
χ202222222-2-2-222-2-2-2222-22000022-2-222-2-2-2-20000-2200000000000000000000000000-222-200000000
χ21222222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-211111111000000000000
χ23222222-122222222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-211-1-11111110000000022-2-2-1-1-1-11111000000000000
χ24222222-122222222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-211-1-111111100000000-2-2221111-1-1-1-1000000000000
χ25222222-12-2-2-2-2222-1-1-1-2-22222-1-11111-1-1-1-1-2-21111-1-1-1-111000000002-22-2-1-111-1-111000000000000
χ26222222-12-2-2-2-2222-1-1-1-2-22222-1-11111-1-1-1-1-2-21111-1-1-1-11100000000-22-2211-1-111-1-1000000000000
χ27222222-12-2-2-2-2222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-122-1-1111111-1-1000000002-2-22-1-11111-1-1000000000000
χ28222222-12-2-2-2-2222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-122-1-1111111-1-100000000-222-211-1-1-1-111000000000000
χ292222-2-22222-2-22-2-2222-2222-2-2-2-222-2-22-2-222-222-2222-2-2-2-200000000000000000000000000000000
χ302222-2-22222-2-22-2-2222-22-2-222-2-222-2-22-2-22-22-2-2-22-2-2222200000000000000000000000000000000
χ312222-2-222-2-2222-2-22222-222-2-2-2-2-2-2222-2-22-22-2-22-222-2-22200000000000000000000000000000000
χ322222-2-222-2-2222-2-22222-2-2-222-2-2-2-2222-2-222-2222-2-2-222-2-200000000000000000000000000000000
χ332222-2-22-22222-222222-2-20000-2-22222-222-20000-2-20000000000000000000000000000002-22-20000
χ342222-2-22-22222-222222-2-20000-2-22222-222-20000-2-2000000000000000000000000000000-22-220000
χ352222-2-22-2-2-2-2-2-222222220000-2-2-2-2-2-2-222-20000220000000000000000000000000000002-2-220000
χ362222-2-22-2-2-2-2-2-222222220000-2-2-2-2-2-2-222-2000022000000000000000000000000000000-222-20000
χ372222-2-2-1222-2-22-2-2-1-1-1-2222-2-211-1-111-111-12-2-1-11-1-1-11111000000000000−i3i3−i3i3−i3i3−i3i3000000000000
χ382222-2-2-1222-2-22-2-2-1-1-1-2222-2-211-1-111-111-12-2-1-11-1-1-11111000000000000i3−i3i3−i3i3−i3i3−i3000000000000
χ392222-2-2-1222-2-22-2-2-1-1-1-22-2-22211-1-111-111-1-22111-111-1-1-1-1000000000000−i3i3−i3i3i3−i3i3−i3000000000000
χ402222-2-2-1222-2-22-2-2-1-1-1-22-2-22211-1-111-111-1-22111-111-1-1-1-1000000000000i3−i3i3−i3−i3i3−i3i3000000000000
χ412222-2-2-12-2-2222-2-2-1-1-12-222-2-21111-1-1-111-1-2211-11-1-111-1-1000000000000−i3i3i3−i3−i3i3i3−i3000000000000
χ422222-2-2-12-2-2222-2-2-1-1-12-222-2-21111-1-1-111-1-2211-11-1-111-1-1000000000000i3−i3−i3i3i3−i3−i3i3000000000000
χ432222-2-2-12-2-2222-2-2-1-1-12-2-2-2221111-1-1-111-12-2-1-1-1111-1-111000000000000−i3i3i3−i3i3−i3−i3i3000000000000
χ442222-2-2-12-2-2222-2-2-1-1-12-2-2-2221111-1-1-111-12-2-1-1-1111-1-111000000000000i3−i3−i3i3−i3i3i3−i3000000000000
χ4522-2-22-2220000-22-2-2-22002i−2i2i−2i2-2000022-2-20000002i−2i2i−2i00000022-2-200000000000000000000002i−2i
χ4622-2-22-2220000-22-2-2-22002i−2i2i−2i2-2000022-2-20000002i−2i2i−2i000000-2-2220000000000000000000000−2i2i
χ4722-2-22-2220000-22-2-2-2200−2i2i−2i2i2-2000022-2-2000000−2i2i−2i2i00000022-2-20000000000000000000000−2i2i
χ4822-2-22-2220000-22-2-2-2200−2i2i−2i2i2-2000022-2-2000000−2i2i−2i2i000000-2-22200000000000000000000002i−2i
χ4922-2-2-22220000-2-22-2-22002i−2i−2i2i-2200002-22-20000002i−2i−2i2i0022-2-20000000000000000000000002i−2i00
χ5022-2-2-22220000-2-22-2-22002i−2i−2i2i-2200002-22-20000002i−2i−2i2i00-2-222000000000000000000000000−2i2i00
χ5122-2-2-22220000-2-22-2-2200−2i2i2i−2i-2200002-22-2000000−2i2i2i−2i0022-2-2000000000000000000000000−2i2i00
χ5222-2-2-22220000-2-22-2-2200−2i2i2i−2i-2200002-22-2000000−2i2i2i−2i00-2-2220000000000000000000000002i−2i00
χ53444444-2-444-4-4-4-4-4-2-2-24-40000-2-2-2-22222220000-2200000000000000000000000000000000000000
χ54444444-2-4-4-444-4-4-4-2-2-2-440000-2-222-2-2222200002-200000000000000000000000000000000000000
χ554444-4-4-2-44444-444-2-2-2-4-4000022-2-2-2-22-2-2200002200000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-4-444-2-2-24400002222222-2-220000-2-200000000000000000000000000000000000000
χ5744-4-44-44-400004-44-4-440000004-40000-4-44400000000000000000000000000000000000000000000
χ5844-4-44-4-240000-44-422-2004i−4i4i−4i-220000-2-222000000−2i2i−2i2i0000000000000000000000000000000000
χ5944-4-44-4-240000-44-422-200−4i4i−4i4i-220000-2-2220000002i−2i2i−2i0000000000000000000000000000000000
χ6044-4-44-4-2-400004-4422-2000000-22000022-2-200−2i32i3000000−2i32i300000000000000000000000000000000
χ6144-4-44-4-2-400004-4422-2000000-22000022-2-2002i3−2i30000002i3−2i300000000000000000000000000000000
χ6244-4-4-444-4000044-4-4-44000000-440000-44-4400000000000000000000000000000000000000000000
χ6344-4-4-44-240000-4-4422-2004i−4i−4i4i2-20000-22-22000000−2i2i2i−2i0000000000000000000000000000000000
χ6444-4-4-44-240000-4-4422-200−4i4i4i−4i2-20000-22-220000002i−2i−2i2i0000000000000000000000000000000000
χ6544-4-4-44-2-4000044-422-20000002-200002-22-200−2i32i30000002i3−2i300000000000000000000000000000000
χ6644-4-4-44-2-4000044-422-20000002-200002-22-2002i3−2i3000000−2i32i300000000000000000000000000000000
χ674-44-40040004-40004-4-400000000004-400000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ684-44-40040004-40004-4-400000000004-40000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ694-44-4004000-440004-4-40000000000-4400000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ704-44-4004000-440004-4-40000000000-440000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ714-4-4400404-400000-44-4000000004-40000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ724-4-4400404-400000-44-4000000004-4000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ734-4-440040-4400000-44-400000000-440000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ744-4-440040-4400000-44-400000000-44000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ758-88-800-40008-8000-4440000000000-44000000000000000000000000000000000000000000000000
χ768-88-800-4000-88000-44400000000004-4000000000000000000000000000000000000000000000000
χ778-8-8800-408-8000004-4400000000-4400000000000000000000000000000000000000000000000000
χ788-8-8800-40-88000004-44000000004-400000000000000000000000000000000000000000000000000

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