Finite Group Databasebeta

← Group #10848626

Character table — Group #10848626

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order122222344444444666446612121212121212122244888812122424242424242424444444444444668812122424242424444424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-11111-1-1-1
χ91111111-1-1-1-11111111-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-111-1-1-111-1-1-11-1
χ101111111-1-1-1-11111111-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-11-1-1111-11
χ111111111-1-1-1-11111111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-11-1-1-1-111-111-1-1-1-11
χ121111111-1-1-1-11111111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-1-1-1111-1-11111-1
χ131111111-1-1-1-11111111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1111-1-111-1-1-111-1-11
χ141111111-1-1-1-11111111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111111-1-111-1
χ151111111-1-1-1-11111111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-11-11111-1-1-1-1-111-11-1
χ161111111-1-1-1-11111111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11111-1-1111-1-11-11
χ17222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-22-22-200002-2000000000000000000002-2002-2000000000000
χ18222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-2-22-2200002-200000000000000000000-2200-22000000000000
χ192222222-2-222-2-2-2-2222-2222-2-222-2-2-2-22-2-220000-22000000000000000000002-200-22000000000000
χ202222222-2-222-2-2-2-2222-2222-2-222-2-2-2-2-222-20000-2200000000000000000000-22002-2000000000000
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000000000000-1-122-1-1-1-1-1-100000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111000000000000-1-1-2-2-1-1111100000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000000011-2-211111100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000000000000112211-1-1-1-100000000
χ25222222-122-2-2-2-2-2-2-1-1-12-2-1-1-1-11111112-22-20000-1133−3−333−3−3000000000000-1100-113−33−300000000
χ26222222-122-2-2-2-2-2-2-1-1-12-2-1-1-1-11111112-22-20000-11−3−333−3−333000000000000-1100-11−33−3300000000
χ27222222-122-2-2-2-2-2-2-1-1-12-2-1-1-1-1111111-22-220000-1133−3−333−3−30000000000001-1001-1−33−3300000000
χ28222222-122-2-2-2-2-2-2-1-1-12-2-1-1-1-1111111-22-220000-11−3−333−3−3330000000000001-1001-13−33−300000000
χ29222222-1-2-222-2-2-2-2-1-1-1-22-1-111-1-111112-2-2200001-133−3−3−3−333000000000000-11001-13−3−3300000000
χ30222222-1-2-222-2-2-2-2-1-1-1-22-1-111-1-111112-2-2200001-1−3−33333−3−3000000000000-11001-1−333−300000000
χ31222222-1-2-222-2-2-2-2-1-1-1-22-1-111-1-11111-222-200001-133−3−3−3−3330000000000001-100-11−333−300000000
χ32222222-1-2-222-2-2-2-2-1-1-1-22-1-111-1-11111-222-200001-1−3−33333−3−30000000000001-100-113−3−3300000000
χ33222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-122-2-222-2-211-1-1-1-11111000000000000-1-12-211-1-11100000000
χ34222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-122-2-2-2-222111111-1-1-1-1000000000000-1-1-221111-1-100000000
χ35222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-1-2-22222-2-211-1-1-1-1111100000000000011-22-1-111-1-100000000
χ36222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-1-2-222-2-222111111-1-1-1-1000000000000112-2-1-1-1-11100000000
χ372222-2-222222-222-2222-2-2-2-22222-222-200000000-2-200000000000000000000000000000002-22-2000
χ382222-2-222222-222-2222-2-2-2-22222-222-200000000-2-20000000000000000000000000000000-22-22000
χ392222-2-2222-2-22-2-22222-22-2-222-2-22-2-2200000000-220000000022-2-200000000000000000020000-200
χ402222-2-2222-2-22-2-22222-22-2-222-2-22-2-2200000000-2200000000-2-222000000000000000000-20000200
χ412222-2-22-2-2222-2-222222-2-2-2-2-2222-2-22000000002-20000000022-2-2000000000000000000-20000200
χ422222-2-22-2-2222-2-222222-2-2-2-2-2222-2-22000000002-200000000-2-22200000000000000000020000-200
χ432222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-222-2000000002200000000000000000000000000000002-2-22000
χ442222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-222-200000000220000000000000000000000000000000-222-2000
χ452-2-222-22000022-2-2-2-22002-2000022-2-20000002i−2i0000002i−2i2i−2i2i−2i2i−2i000022-2-2000000000000000000
χ462-2-222-22000022-2-2-2-22002-2000022-2-20000002i−2i0000002i−2i2i−2i−2i2i−2i2i0000-2-222000000000000000000
χ472-2-222-22000022-2-2-2-22002-2000022-2-2000000−2i2i000000−2i2i−2i2i2i−2i2i−2i0000-2-222000000000000000000
χ482-2-222-22000022-2-2-2-22002-2000022-2-2000000−2i2i000000−2i2i−2i2i−2i2i−2i2i000022-2-2000000000000000000
χ492-2-22-22200002-22-2-2-2200-2200002-22-200002i−2i00002i−2i2i−2i00002i−2i−2i2i22-2-20000000000000000000000
χ502-2-22-22200002-22-2-2-2200-2200002-22-200002i−2i00002i−2i2i−2i0000−2i2i2i−2i-2-2220000000000000000000000
χ512-2-22-22200002-22-2-2-2200-2200002-22-20000−2i2i0000−2i2i−2i2i00002i−2i−2i2i-2-2220000000000000000000000
χ522-2-22-22200002-22-2-2-2200-2200002-22-20000−2i2i0000−2i2i−2i2i0000−2i2i2i−2i22-2-20000000000000000000000
χ534444-4-4-24444-444-4-2-2-2-4-422-2-2-2-22-2-22000000002200000000000000000000000000000000000000
χ544444-4-4-244-4-44-4-44-2-2-2-4422-2-222-222-2000000002-200000000000000000000000000000000000000
χ554444-4-4-2-4-4444-4-44-2-2-24-42222-2-2-222-200000000-2200000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-444-4-2-2-2442222222-2-2200000000-2-200000000000000000000000000000000000000
χ5744-4-4004004i−4i00004-4-40000004i−4i000000000000000000000000002-22-22i−2i2i−2i000000000000000000
χ5844-4-4004004i−4i00004-4-40000004i−4i00000000000000000000000000-22-22−2i2i−2i2i000000000000000000
χ5944-4-400400−4i4i00004-4-4000000−4i4i000000000000000000000000002-22-2−2i2i−2i2i000000000000000000
χ6044-4-400400−4i4i00004-4-4000000−4i4i00000000000000000000000000-22-222i−2i2i−2i000000000000000000
χ614-44-40044i−4i000000-44-400004i−4i00000000000000000000000000002-2-222i−2i−2i2i000000000000000000
χ624-44-40044i−4i000000-44-400004i−4i0000000000000000000000000000-222-2−2i2i2i−2i000000000000000000
χ634-44-4004−4i4i000000-44-40000−4i4i00000000000000000000000000002-2-22−2i2i2i−2i000000000000000000
χ644-44-4004−4i4i000000-44-40000−4i4i0000000000000000000000000000-222-22i−2i−2i2i000000000000000000
χ654-4-444-440000-4-444-4-44004-40000-4-444000000000000000000000000000000000000000000000000
χ664-4-444-4-2000044-4-422-200-220000-2-2220000004i−4i000000−2i2i−2i2i000000000000000000000000000000
χ674-4-444-4-2000044-4-422-200-220000-2-222000000−4i4i0000002i−2i2i−2i000000000000000000000000000000
χ684-4-444-4-20000-4-44422-200-22000022-2-200000000000000−2i32i32i3−2i3000000000000000000000000000000
χ694-4-444-4-20000-4-44422-200-22000022-2-2000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ704-4-44-4440000-44-44-4-4400-440000-44-44000000000000000000000000000000000000000000000000
χ714-4-44-44-200004-44-422-2002-20000-22-2200004i−4i0000−2i2i−2i2i0000000000000000000000000000000000
χ724-4-44-44-200004-44-422-2002-20000-22-220000−4i4i00002i−2i2i−2i0000000000000000000000000000000000
χ734-4-44-44-20000-44-4422-2002-200002-22-20000000000−2i32i32i3−2i30000000000000000000000000000000000
χ744-4-44-44-20000-44-4422-2002-200002-22-200000000002i3−2i3−2i32i30000000000000000000000000000000000
χ7588-8-800-4008i−8i0000-444000000−4i4i0000000000000000000000000000000000000000000000000000
χ7688-8-800-400−8i8i0000-4440000004i−4i0000000000000000000000000000000000000000000000000000
χ778-88-800-48i−8i0000004-440000−4i4i000000000000000000000000000000000000000000000000000000
χ788-88-800-4−8i8i0000004-4400004i−4i000000000000000000000000000000000000000000000000000000

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