Finite Group Databasebeta

← Group #10849401

Character table — Group #10849401

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888881212121212121212161616161616161616161616242424242424242424242424
order122222344444444666444444661212121212121212246612121212121212124444444444881212121224242424224444448888
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
χ51111111111111111111-1-11-1-11111111111-1-1-1-11-1-1-1-11-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111-1-11-1-11111111111-1-1-1-11-1-1-1-11-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ71111111111111111111-1-11-1-11111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111111-1-11-1-11111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111
χ91111111-1-11-1-1111111-111-11111111-1-1-1-11-1-1-1-1-111-1-1-1111111-1-1-1-11-11-111-1-111-1-11-11-111-1-111-1-1
χ101111111-1-11-1-1111111-111-11111111-1-1-1-11-1-1-1-1-111-1-1-1111111-1-1-1-1-11-11-1-111-1-111-11-11-1-11111-1-1
χ111111111-1-11-1-1111111-111-11111111-1-1-1-11-1-1-1-1-111-1-1-111-1-1-1-111111-11-111-1-111-1-1-11-11-1-111-1-111
χ121111111-1-11-1-1111111-111-11111111-1-1-1-11-1-1-1-1-111-1-1-111-1-1-1-11111-11-11-1-111-1-1111-11-111-1-1-1-111
χ131111111-1-11-1-1111111-1-1-1-1-1-111111-1-1-1-111111-1-1-111-1-1-11111-1-1-1-11-1-1111-1-1-1-111-11-1111-1-1-1-111
χ141111111-1-11-1-1111111-1-1-1-1-1-111111-1-1-1-111111-1-1-111-1-1-11111-1-1-1-1-111-1-1-11111-1-11-11-1-1-111-1-111
χ151111111-1-11-1-1111111-1-1-1-1-1-111111-1-1-1-111111-1-1-111-1-1-1-1-1-1-111111-1-1111-1-1-1-1111-11-1-1-11111-1-1
χ161111111-1-11-1-1111111-1-1-1-1-1-111111-1-1-1-111111-1-1-111-1-1-1-1-1-1-11111-111-1-1-11111-1-1-11-1111-1-111-1-1
χ17222222222-2-2-2-2-2-2222200-20022-2-2-222-2-2-2000020000-2000000000000000000000000002-22-20000
χ18222222222-2-2-2-2-2-2222200-20022-2-2-222-2-2-2000020000-200000000000000000000000000-22-220000
χ192222222-2-2-222-2-2-2222-20020022-2-2-2-2-222-20000-200002000000000000000000000000002-2-220000
χ202222222-2-2-222-2-2-2222-20020022-2-2-2-2-222-20000-20000200000000000000000000000000-222-20000
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
χ23222222-122222222-1-1-12-2-22-2-2-1-1-1-1-1-1-1-1-1-1-2-211-11111-1110000000022-2-2-1-1-1-11111000000000000
χ24222222-122222222-1-1-12-2-22-2-2-1-1-1-1-1-1-1-1-1-1-2-211-11111-11100000000-2-2221111-1-1-1-1000000000000
χ25222222-1-2-22-2-2222-1-1-1-222-222-1-1-1-1-11111-1-2-2111-1-1111-1-1000000002-22-2-1-111-1-111000000000000
χ26222222-1-2-22-2-2222-1-1-1-222-222-1-1-1-1-11111-1-2-2111-1-1111-1-100000000-22-2211-1-111-1-1000000000000
χ27222222-1-2-22-2-2222-1-1-1-2-2-2-2-2-2-1-1-1-1-11111-122-1-1111-1-1111000000002-2-22-1-11111-1-1000000000000
χ28222222-1-2-22-2-2222-1-1-1-2-2-2-2-2-2-1-1-1-1-11111-122-1-1111-1-111100000000-222-211-1-1-1-111000000000000
χ292222-2-22222-2-22-2-2222-2222-2-2-2-22-2-222-2-222-222-222-2-22-2-200000000000000000000000000000000
χ302222-2-22222-2-22-2-2222-2-2-2222-2-22-2-222-2-22-22-2-2-2-2-22222200000000000000000000000000000000
χ312222-2-2222-222-222222-200-200-2-2-2222222-20000-20000-2000000000000000000000022-2-200000000
χ322222-2-2222-222-222222-200-200-2-2-2222222-20000-20000-20000000000000000000000-2-22200000000
χ332222-2-22-2-22222-2-2222222-2-2-2-2-22-2-2-2-2222-22-2-222222-2-2-200000000000000000000000000000000
χ342222-2-22-2-22222-2-22222-2-2-222-2-22-2-2-2-22222-2222-2-2-2-2-22200000000000000000000000000000000
χ352222-2-22-2-2-2-2-2-222222200200-2-2-222-2-2-2-2-2000020000200000000000000000000002-2-2200000000
χ362222-2-22-2-2-2-2-2-222222200200-2-2-222-2-2-2-2-200002000020000000000000000000000-222-200000000
χ372222-2-2-1222-2-22-2-2-1-1-1-2222-2-211-111-1-111-12-2-1-11-1-111-111000000000000−i3i3−i3i3−i3i3−i3i3000000000000
χ382222-2-2-1222-2-22-2-2-1-1-1-2222-2-211-111-1-111-12-2-1-11-1-111-111000000000000i3−i3i3−i3i3−i3i3−i3000000000000
χ392222-2-2-1222-2-22-2-2-1-1-1-2-2-222211-111-1-111-1-2211111-1-1-1-1-1000000000000−i3i3−i3i3i3−i3i3−i3000000000000
χ402222-2-2-1222-2-22-2-2-1-1-1-2-2-222211-111-1-111-1-2211111-1-1-1-1-1000000000000i3−i3i3−i3−i3i3−i3i3000000000000
χ412222-2-2-1-2-22222-2-2-1-1-1222-2-2-211-11111-1-1-1-2211-1-1-1-1-1111000000000000−i3i3i3−i3−i3i3i3−i3000000000000
χ422222-2-2-1-2-22222-2-2-1-1-1222-2-2-211-11111-1-1-1-2211-1-1-1-1-1111000000000000i3−i3−i3i3i3−i3−i3i3000000000000
χ432222-2-2-1-2-22222-2-2-1-1-12-2-2-22211-11111-1-1-12-2-1-1-111111-1-1000000000000−i3i3i3−i3i3−i3−i3i3000000000000
χ442222-2-2-1-2-22222-2-2-1-1-12-2-2-22211-11111-1-1-12-2-1-1-111111-1-1000000000000i3−i3−i3i3−i3i3i3−i3000000000000
χ452-22-22-2200-20022-22-2-202i−2i02i−2i2-2-22-200002000002i−2i0002i−2i000022-2-200000000000000000000002i−2i
χ462-22-22-2200-20022-22-2-202i−2i02i−2i2-2-22-200002000002i−2i0002i−2i0000-2-2220000000000000000000000−2i2i
χ472-22-22-2200-20022-22-2-20−2i2i0−2i2i2-2-22-20000200000−2i2i000−2i2i000022-2-20000000000000000000000−2i2i
χ482-22-22-2200-20022-22-2-20−2i2i0−2i2i2-2-22-20000200000−2i2i000−2i2i0000-2-22200000000000000000000002i−2i
χ492-22-2-22200-2002-222-2-202i−2i0−2i2i-22-2-2200002000002i−2i000−2i2i22-2-20000000000000000000000002i−2i00
χ502-22-2-22200-2002-222-2-202i−2i0−2i2i-22-2-2200002000002i−2i000−2i2i-2-222000000000000000000000000−2i2i00
χ512-22-2-22200-2002-222-2-20−2i2i02i−2i-22-2-220000200000−2i2i0002i−2i22-2-2000000000000000000000000−2i2i00
χ522-22-2-22200-2002-222-2-20−2i2i02i−2i-22-2-220000200000−2i2i0002i−2i-2-2220000000000000000000000002i−2i00
χ53444444-244-4-4-4-4-4-4-2-2-2400-400-2-2222-2-22220000-2000020000000000000000000000000000000000
χ54444444-2-4-4-444-4-4-4-2-2-2-400400-2-222222-2-22000020000-20000000000000000000000000000000000
χ554444-4-4-244-444-444-2-2-2-400-400222-2-2-2-2-2-2200002000020000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-4-444-2-2-2400400222-2-2222220000-20000-20000000000000000000000000000000000
χ5744-4-40044-4000000-44-4000000000004-40000000000000002-22-22-22-2000000000000000000000000
χ5844-4-40044-4000000-44-4000000000004-4000000000000000-22-22-22-22000000000000000000000000
χ5944-4-4004-44000000-44-400000000000-440000000000000002-22-2-22-22000000000000000000000000
χ6044-4-4004-44000000-44-400000000000-44000000000000000-22-222-22-2000000000000000000000000
χ614-44-44-4400400-4-444-4-40000004-44-440000-400000000000000000000000000000000000000000000
χ624-44-44-4-200400-4-44-222000000-22-22-20000200−2i32i3000−2i32i300000000000000000000000000000000000
χ634-44-44-4-200400-4-44-222000000-22-22-200002002i3−2i30002i3−2i300000000000000000000000000000000000
χ644-44-44-4-200-40044-4-22204i−4i04i−4i-222-220000-200000−2i2i000−2i2i00000000000000000000000000000000
χ654-44-44-4-200-40044-4-2220−4i4i0−4i4i-222-220000-2000002i−2i0002i−2i00000000000000000000000000000000
χ664-44-4-44400400-44-44-4-4000000-4444-40000-400000000000000000000000000000000000000000000
χ674-44-4-44-200400-44-4-2220000002-2-2-220000200−2i32i30002i3−2i300000000000000000000000000000000000
χ684-44-4-44-200400-44-4-2220000002-2-2-2200002002i3−2i3000−2i32i300000000000000000000000000000000000
χ694-44-4-44-200-4004-44-22204i−4i0−4i4i2-222-20000-200000−2i2i0002i−2i00000000000000000000000000000000
χ704-44-4-44-200-4004-44-2220−4i4i04i−4i2-222-20000-2000002i−2i000−2i2i00000000000000000000000000000000
χ714-4-440040004-4000-4-4400000000000004-400000000000002-2-222-2-22000000000000000000000000
χ724-4-440040004-4000-4-4400000000000004-40000000000000-222-2-222-2000000000000000000000000
χ734-4-44004000-44000-4-440000000000000-4400000000000002-2-22-222-2000000000000000000000000
χ744-4-44004000-44000-4-440000000000000-440000000000000-222-22-2-22000000000000000000000000
χ7588-8-800-48-80000004-4400000000000-4400000000000000000000000000000000000000000000000
χ7688-8-800-4-880000004-44000000000004-400000000000000000000000000000000000000000000000
χ778-8-8800-40008-800044-40000000000000-44000000000000000000000000000000000000000000000
χ788-8-8800-4000-8800044-400000000000004-4000000000000000000000000000000000000000000000

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