Finite Group Databasebeta

← Group #10848602

Character table — Group #10848602

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order12222234444444466644661212121212121212444488881212242424242424242444444444444444121212121212121224444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1
χ91111111-1-1-1-11111111-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-111-1-1-1-111-1-11-1
χ101111111-1-1-1-11111111-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-111-1-111-11
χ111111111-1-1-1-11111111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1111-1-1-1-111-1-111-1-1-11
χ121111111-1-1-1-11111111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1-11111-1-1111-1
χ131111111-1-1-1-11111111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-1-1-111-11
χ141111111-1-1-1-11111111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-1111111-1-11-1
χ151111111-1-1-1-11111111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111111-1-1-11111-1-1-1-1-1-1111-1
χ161111111-1-1-1-11111111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-11111-1-1-11
χ17222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-2000000002-2000000000000000000000000000000002-22-200
χ18222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-2000000002-200000000000000000000000000000000-22-2200
χ192222222-2-222-2-2-2-2222-2222-2-222-2-2-2-200000000-22000000000000000000000000000000002-2-2200
χ202222222-2-222-2-2-2-2222-2222-2-222-2-2-2-200000000-2200000000000000000000000000000000-222-200
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111000000000000-2-2-1-1-1-1111100000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000000000000221111-1-1-1-100000000
χ25222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-122-2-222-2-211-1-1-1-111110000000000002-2-1-111-1-11100000000
χ26222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-122-2-2-2-222111111-1-1-1-1000000000000-22-1-11111-1-100000000
χ27222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-1-2-22222-2-211-1-1-1-11111000000000000-2211-1-111-1-100000000
χ28222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-1-2-222-2-222111111-1-1-1-10000000000002-211-1-1-1-11100000000
χ292222-2-222222-222-2222-2-2-2-22222-2-2222-22-20000-2-200000000000000000000002-22-2000000000000
χ302222-2-222222-222-2222-2-2-2-22222-2-222-22-220000-2-20000000000000000000000-22-22000000000000
χ312222-2-2222-2-22-2-22222-22-2-222-2-222-2-200000000-220000000022-2-20000000000000000002-2000000
χ322222-2-2222-2-22-2-22222-22-2-222-2-222-2-200000000-2200000000-2-222000000000000000000-22000000
χ332222-2-22-2-2222-2-222222-2-2-2-2-22222-2-2000000002-20000000022-2-2000000000000000000-22000000
χ342222-2-22-2-2222-2-222222-2-2-2-2-22222-2-2000000002-200000000-2-2220000000000000000002-2000000
χ352222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-2-2222-2-2200002200000000000000000000002-2-22000000000000
χ362222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-2-222-222-20000220000000000000000000000-222-2000000000000
χ372222-2-2-12222-222-2-1-1-1-2-211-1-1-1-111-1-12-22-2000011−i3−i3i3i3−i3−i3i3i300000000000000-11-11−i3i3−i3i300000000
χ382222-2-2-12222-222-2-1-1-1-2-211-1-1-1-111-1-12-22-2000011i3i3−i3−i3i3i3−i3−i300000000000000-11-11i3−i3i3−i300000000
χ392222-2-2-12222-222-2-1-1-1-2-211-1-1-1-111-1-1-22-22000011−i3−i3i3i3−i3−i3i3i3000000000000001-11-1i3−i3i3−i300000000
χ402222-2-2-12222-222-2-1-1-1-2-211-1-1-1-111-1-1-22-22000011i3i3−i3−i3i3i3−i3−i3000000000000001-11-1−i3i3−i3i300000000
χ412222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-12-2-220000-1-1−i3−i3i3i3i3i3−i3−i300000000000000-111-1−i3i3i3−i300000000
χ422222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-12-2-220000-1-1i3i3−i3−i3−i3−i3i3i300000000000000-111-1i3−i3−i3i300000000
χ432222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-1-222-20000-1-1−i3−i3i3i3i3i3−i3−i3000000000000001-1-11i3−i3−i3i300000000
χ442222-2-2-1-2-2-2-2-222-2-1-1-12211111111-1-1-222-20000-1-1i3i3−i3−i3−i3−i3i3i3000000000000001-1-11−i3i3i3−i300000000
χ452-2-222-22000022-2-2-2-22002-200002-22-20000002i−2i0000002i−2i2i−2i2i−2i2i−2i000022-2-2000000000000000000
χ462-2-222-22000022-2-2-2-22002-200002-22-20000002i−2i0000002i−2i2i−2i−2i2i−2i2i0000-2-222000000000000000000
χ472-2-222-22000022-2-2-2-22002-200002-22-2000000−2i2i000000−2i2i−2i2i2i−2i2i−2i0000-2-222000000000000000000
χ482-2-222-22000022-2-2-2-22002-200002-22-2000000−2i2i000000−2i2i−2i2i−2i2i−2i2i000022-2-2000000000000000000
χ492-2-22-22200002-22-2-2-2200-2200002-2-2200002i−2i00002i−2i2i−2i00002i−2i−2i2i22-2-20000000000000000000000
χ502-2-22-22200002-22-2-2-2200-2200002-2-2200002i−2i00002i−2i2i−2i0000−2i2i2i−2i-2-2220000000000000000000000
χ512-2-22-22200002-22-2-2-2200-2200002-2-220000−2i2i0000−2i2i−2i2i00002i−2i−2i2i-2-2220000000000000000000000
χ522-2-22-22200002-22-2-2-2200-2200002-2-220000−2i2i0000−2i2i−2i2i0000−2i2i2i−2i22-2-20000000000000000000000
χ53444444-244-4-4-4-4-4-4-2-2-24-4-2-2-2-222222200000000-2200000000000000000000000000000000000000
χ54444444-2-4-444-4-4-4-4-2-2-2-44-2-222-2-22222000000002-200000000000000000000000000000000000000
χ554444-4-4-244-4-44-4-44-2-2-2-4422-2-222-2-222000000002-200000000000000000000000000000000000000
χ564444-4-4-2-4-4444-4-44-2-2-24-42222-2-2-2-22200000000-2200000000000000000000000000000000000000
χ5744-4-4004004-400004-4-40000004-4000000000000000000000000002-22-22-22-2000000000000000000
χ5844-4-4004004-400004-4-40000004-400000000000000000000000000-22-22-22-22000000000000000000
χ5944-4-400400-4400004-4-4000000-44000000000000000000000000002-22-2-22-22000000000000000000
χ6044-4-400400-4400004-4-4000000-4400000000000000000000000000-22-222-22-2000000000000000000
χ614-44-40044-4000000-44-400004-400000000000000000000000000002-2-222-2-22000000000000000000
χ624-44-40044-4000000-44-400004-40000000000000000000000000000-222-2-222-2000000000000000000
χ634-44-4004-44000000-44-40000-4400000000000000000000000000002-2-22-222-2000000000000000000
χ644-44-4004-44000000-44-40000-440000000000000000000000000000-222-22-2-22000000000000000000
χ654-4-444-440000-4-444-4-44004-40000-44-44000000000000000000000000000000000000000000000000
χ664-4-444-4-2000044-4-422-200-220000-22-220000004i−4i000000−2i2i−2i2i000000000000000000000000000000
χ674-4-444-4-2000044-4-422-200-220000-22-22000000−4i4i0000002i−2i2i−2i000000000000000000000000000000
χ684-4-444-4-20000-4-44422-200-2200002-22-2000000000023−23−23230000000000000000000000000000000000
χ694-4-444-4-20000-4-44422-200-2200002-22-20000000000−232323−230000000000000000000000000000000000
χ704-4-44-4440000-44-44-4-4400-440000-444-4000000000000000000000000000000000000000000000000
χ714-4-44-44-200004-44-422-2002-20000-222-200004i−4i0000−2i2i−2i2i0000000000000000000000000000000000
χ724-4-44-44-200004-44-422-2002-20000-222-20000−4i4i00002i−2i2i−2i0000000000000000000000000000000000
χ734-4-44-44-20000-44-4422-2002-200002-2-220000000000000023−23−2323000000000000000000000000000000
χ744-4-44-44-20000-44-4422-2002-200002-2-2200000000000000−232323−23000000000000000000000000000000
χ7588-8-800-4008-80000-444000000-440000000000000000000000000000000000000000000000000000
χ7688-8-800-400-880000-4440000004-40000000000000000000000000000000000000000000000000000
χ778-88-800-48-80000004-440000-44000000000000000000000000000000000000000000000000000000
χ788-88-800-4-880000004-4400004-4000000000000000000000000000000000000000000000000000000

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