Finite Group Databasebeta

← Group #10833375

Character table — Group #10833375

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222222234444446662466661212121212122444688881224242424242424242244444444444461212121212121224444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1111111-1-1
χ411111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-11-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111
χ7111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1111-1-11-1-111
χ8111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-111-111-111-1-1
χ911111-1-1111-1-1111111-1-111-1-1111-1-111-1-11-111-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1111-1-1-1-1-1-1111-1
χ1011111-1-1111-1-1111111-1-111-1-1111-1-111-1-11-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1111-1-11111-1-1-11
χ1111111-1-1111-1-1111111-1-111-1-1111-1-111-1-11-1-1-111-1-1-1-1-111111111-1-1-1-11111-111-1-1-1-1111-1-1-1-111-11
χ1211111-1-1111-1-1111111-1-111-1-1111-1-111-1-11-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111111-1-11-1
χ1311111-1-1111-1-1111111-1-111-1-1111-1-11-111-1-111-1-1-11111-1-1-1-111111111-1-1-1-1-11-111-1-1-111-111-1-1-1-11
χ1411111-1-1111-1-1111111-1-111-1-1111-1-11-111-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-111-1-1-1111-1-11111-1
χ1511111-1-1111-1-1111111-1-111-1-1111-1-11-111-1-1-1-111-1-1-1-1-111111111-1-1-1-111111-1-11111-1-1-1-111-1-1-11-1
χ1611111-1-1111-1-1111111-1-111-1-1111-1-11-111-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11111-1-1-11-1-1111-11
χ17222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-2000020000-200000000000000000000000000000002-202-200
χ18222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-2000020000-20000000000000000000000000000000-220-2200
χ1922222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ2022222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-111111111000000000000-2-2-1-1-111-11100000000
χ2122222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ2222222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-11111111100000000000022111-1-11-1-100000000
χ2322222-2-222-222-2-2-2222-2222-2-2-2-2-222-20000-20000200000000000000000000000000000002-20-2200
χ2422222-2-222-222-2-2-2222-2222-2-2-2-2-222-20000-2000020000000000000000000000000000000-2202-200
χ2522222-2-22-12-2-2222-1-1-1-2-2-1-111-1-1-111-12-2-22122-2-21-1-1-1-111110000000000002-2-111-1-1-11100000000
χ2622222-2-22-12-2-2222-1-1-1-2-2-1-111-1-1-111-12-2-221-2-22211111-1-1-1-1000000000000-22-11111-1-1-100000000
χ2722222-2-22-12-2-2222-1-1-1-2-2-1-111-1-1-111-1-222-2122-2-21-1-1-1-11111000000000000-221-1-1111-1-100000000
χ2822222-2-22-12-2-2222-1-1-1-2-2-1-111-1-1-111-1-222-21-2-22211111-1-1-1-10000000000002-21-1-1-1-111100000000
χ292222-222-222222-2-2222-2-2-2-2222-2-222222-2-2-20000-2000000000000000000000022-200-20000000000
χ302222-222-222222-2-2222-2-2-2-2222-2-2222-2-222-20000-20000000000000000000000-2-220020000000000
χ312222-222-22-2-2-2-222222-22-2-222-222-2-2-20000-2000020000000022-2-2000000000000000000200-20000
χ322222-222-22-2-2-2-222222-22-2-222-222-2-2-20000-20000200000000-2-222000000000000000000-20020000
χ332222-222-2-12222-2-2-1-1-1-2-211-1-1-111-1-1-122-2-2100001−i3−i3i3i3−i3−i3i3i300000000000000-1-11−i3i31−i3i300000000
χ342222-222-2-12222-2-2-1-1-1-2-211-1-1-111-1-1-122-2-2100001i3i3−i3−i3i3i3−i3−i300000000000000-1-11i3−i31i3−i300000000
χ352222-222-2-12222-2-2-1-1-1-2-211-1-1-111-1-1-1-2-222100001−i3−i3i3i3−i3−i3i3i30000000000000011-1i3−i3-1i3−i300000000
χ362222-222-2-12222-2-2-1-1-1-2-211-1-1-111-1-1-1-2-222100001i3i3−i3−i3i3i3−i3−i30000000000000011-1−i3i3-1−i3i300000000
χ372222-2-2-2-222-2-22-2-222222-2-2-2-22-2-2-2-222-22-220000200000000000000000000002-2200-20000000000
χ382222-2-2-2-222-2-22-2-222222-2-2-2-22-2-2-2-22-22-222000020000000000000000000000-22-20020000000000
χ392222-2-2-2-22-222-2222222-2-2-2-2-2-22222-2000020000-20000000022-2-2000000000000000000-20020000
χ402222-2-2-2-22-222-2222222-2-2-2-2-2-22222-2000020000-200000000-2-222000000000000000000200-20000
χ412222-2-2-2-2-12-2-22-2-2-1-1-1221111-11111-12-22-2-10000-1−i3−i3i3i3i3i3−i3−i300000000000000-11-1−i3i31i3−i300000000
χ422222-2-2-2-2-12-2-22-2-2-1-1-1221111-11111-12-22-2-10000-1i3i3−i3−i3−i3−i3i3i300000000000000-11-1i3−i31−i3i300000000
χ432222-2-2-2-2-12-2-22-2-2-1-1-1221111-11111-1-22-22-10000-1−i3−i3i3i3i3i3−i3−i3000000000000001-11i3−i3-1−i3i300000000
χ442222-2-2-2-2-12-2-22-2-2-1-1-1221111-11111-1-22-22-10000-1i3i3−i3−i3−i3−i3i3i3000000000000001-11−i3i3-1i3−i300000000
χ452-2-22200-22200-22-2-2-22002-20022-200-2000002i−2i0002i−2i2i−2i00002-22-22i2i−2i−2i0000000000000000000000
χ462-2-22200-22200-22-2-2-22002-20022-200-2000002i−2i0002i−2i2i−2i0000-22-22−2i−2i2i2i0000000000000000000000
χ472-2-22200-22200-22-2-2-22002-20022-200-200000−2i2i000−2i2i−2i2i00002-22-2−2i−2i2i2i0000000000000000000000
χ482-2-22200-22200-22-2-2-22002-20022-200-200000−2i2i000−2i2i−2i2i0000-22-222i2i−2i−2i0000000000000000000000
χ492-2-22-20022-20022-2-2-2200-2200-22-200200000002-2000002-22-22-2-22000022-2-2000000000000000000
χ502-2-22-20022-20022-2-2-2200-2200-22-200200000002-2000002-22-2-222-20000-2-222000000000000000000
χ512-2-22-20022-20022-2-2-2200-2200-22-20020000000-2200000-22-222-2-220000-2-222000000000000000000
χ522-2-22-20022-20022-2-2-2200-2200-22-20020000000-2200000-22-22-222-2000022-2-2000000000000000000
χ5344444444-2-4-4-4-4-4-4-2-2-24-4-2-2-2-22222220000-20000200000000000000000000000000000000000000
χ5444444-4-44-2-444-4-4-4-2-2-2-44-2-222222-2-22000020000-200000000000000000000000000000000000000
χ554444-444-4-2-4-4-4-444-2-2-2-4422-2-22-2-2222000020000-200000000000000000000000000000000000000
χ564444-4-4-4-4-2-444-444-2-2-24-422222-2-2-2-220000-20000200000000000000000000000000000000000000
χ5744-4-404-4040000004-4-400004-400000000000000000000000000002-22-22-22-2000000000000000000
χ5844-4-404-4040000004-4-400004-40000000000000000000000000000-22-22-22-22000000000000000000
χ5944-4-40-44040000004-4-40000-4400000000000000000000000000002-22-2-22-22000000000000000000
χ6044-4-40-44040000004-4-40000-440000000000000000000000000000-22-222-22-2000000000000000000
χ614-44-40000404i−4i000-44-40000000004i−4i000000000000000000000002i−2i−2i2i2-2-22000000000000000000
χ624-44-40000404i−4i000-44-40000000004i−4i00000000000000000000000−2i2i2i−2i-222-2000000000000000000
χ634-44-4000040−4i4i000-44-4000000000−4i4i000000000000000000000002i−2i−2i2i-222-2000000000000000000
χ644-44-4000040−4i4i000-44-4000000000−4i4i00000000000000000000000−2i2i2i−2i2-2-22000000000000000000
χ654-4-44400-44-4004-44-4-44004-400-4-44004000000000000000000000000000000000000000000000000
χ664-4-44400-4-2400-44-422-200-2200-2-22002000004i−4i000−2i2i−2i2i0000000000000000000000000000000000
χ674-4-44400-4-2400-44-422-200-2200-2-2200200000−4i4i0002i−2i2i−2i0000000000000000000000000000000000
χ684-4-44400-4-2-4004-4422-200-220022-200-200000000000000−2i32i32i3−2i3000000000000000000000000000000
χ694-4-44400-4-2-4004-4422-200-220022-200-2000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ704-4-44-40044400-4-44-4-4400-44004-4400-4000000000000000000000000000000000000000000000000
χ714-4-44-4004-2400-4-4422-2002-200-22-2002000000000023−23−23230000000000000000000000000000000000
χ724-4-44-4004-2400-4-4422-2002-200-22-20020000000000−232323−230000000000000000000000000000000000
χ734-4-44-4004-2-40044-422-2002-2002-2200-200000004-400000-22-22000000000000000000000000000000
χ744-4-44-4004-2-40044-422-2002-2002-2200-20000000-44000002-22-2000000000000000000000000000000
χ7588-8-808-80-4000000-4440000-44000000000000000000000000000000000000000000000000000000
χ7688-8-80-880-4000000-44400004-4000000000000000000000000000000000000000000000000000000
χ778-88-80000-408i−8i0004-44000000000−4i4i0000000000000000000000000000000000000000000000000
χ788-88-80000-40−8i8i0004-440000000004i−4i0000000000000000000000000000000000000000000000000

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