Finite Group Databasebeta

← Group #10829870

Character table — Group #10829870

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888881212121212121212161616161616161616161616242424242424242424242424
order12222234444444466644444466121212121212121244121212121212121212124444444488882424242424242424224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-111
χ711111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-111
χ811111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ91111111-1-1-1-11111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-11-11-111-1-11-11-1
χ101111111-1-1-1-11111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11-1111-1-1-11-11
χ111111111-1-1-1-11111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-11-11-1-111-11-11
χ121111111-1-1-1-11111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11-1-111-1-1111-11-1-1-1111-11-1
χ131111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-1111-1-11-1-1111-1-11
χ141111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1-111-1-1-111-111-1
χ151111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-111-111-111-1-1-111-1
χ161111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-11-1-1111-1-11-1-11
χ1722222222222-2-2-2-2222-2-222-2-2222222-2-2-2-22-2-2-222-2-222-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-222222222-2-2-2-2-22-2-2-2-222-2-22200000000000000000000000000000000
χ192222222-2-2-2-2-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2-222222-2-2-2-22200000000000000000000000000000000
χ202222222-2-2-2-2-2-2-2-222222-2-22222-2-2-2-2-2-2-2-22-222-2-22222-2-200000000000000000000000000000000
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
χ23222222-122222222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-1111111110000000022-2-2-1-1-1-11111000000000000
χ24222222-122222222-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-1-11111111100000000-2-2221111-1-1-1-1000000000000
χ25222222-12222-2-2-2-2-1-1-1-2-222-2-2-1-1-1-1-1-111112-211-1-111-1-1110000000000003−33−33−33−3000000000000
χ26222222-12222-2-2-2-2-1-1-1-2-222-2-2-1-1-1-1-1-111112-211-1-111-1-111000000000000−33−33−33−33000000000000
χ27222222-12222-2-2-2-2-1-1-1-2-2-2-222-1-1-1-1-1-11111-221111-1-111-1-10000000000003−33−3−33−33000000000000
χ28222222-12222-2-2-2-2-1-1-1-2-2-2-222-1-1-1-1-1-11111-221111-1-111-1-1000000000000−33−333−33−3000000000000
χ29222222-1-2-2-2-22222-1-1-1-2-22222-1-11111-1-1-1-1-2-211-1-1-1-11111000000002-22-2-1-111-1-111000000000000
χ30222222-1-2-2-2-22222-1-1-1-2-22222-1-11111-1-1-1-1-2-211-1-1-1-1111100000000-22-2211-1-111-1-1000000000000
χ31222222-1-2-2-2-22222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-122111111-1-1-1-1000000002-2-22-1-11111-1-1000000000000
χ32222222-1-2-2-2-22222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-122111111-1-1-1-100000000-222-211-1-1-1-111000000000000
χ33222222-1-2-2-2-2-2-2-2-2-1-1-12222-2-2-1-111111111-22-1-1-1-11111-1-10000000000003−3−333−3−33000000000000
χ34222222-1-2-2-2-2-2-2-2-2-1-1-12222-2-2-1-111111111-22-1-1-1-11111-1-1000000000000−333−3−333−3000000000000
χ35222222-1-2-2-2-2-2-2-2-2-1-1-122-2-222-1-1111111112-2-1-111-1-1-1-1110000000000003−3−33−333−3000000000000
χ36222222-1-2-2-2-2-2-2-2-2-1-1-122-2-222-1-1111111112-2-1-111-1-1-1-111000000000000−333−33−3−33000000000000
χ372222-2-2222-2-22-22-22222-20000-2-222-2-22-22-2002-200000000000000000000000000000022000000-2-2
χ382222-2-2222-2-22-22-22222-20000-2-222-2-22-22-2002-2000000000000000000000000000000-2-200000022
χ392222-2-2222-2-2-22-22222-220000-2-222-2-2-22-2200-22000000000000000000000000000022000000-2-200
χ402222-2-2222-2-2-22-22222-220000-2-222-2-2-22-2200-220000000000000000000000000000-2-20000002200
χ412222-2-22-2-2222-22-2222-220000-2-2-2-2222-22-200-220000000000000000000000000000002-2000000-22
χ422222-2-22-2-2222-22-2222-220000-2-2-2-2222-22-200-22000000000000000000000000000000-220000002-2
χ432222-2-22-2-222-22-222222-20000-2-2-2-222-22-22002-200000000000000000000000000002-2000000-2200
χ442222-2-22-2-222-22-222222-20000-2-2-2-222-22-22002-20000000000000000000000000000-220000002-200
χ452-22-22-2200002-2-22-22-2002i−2i2i−2i2-200002-2-2200002i−2i2i−2i000000002i2i−2i−2i0000000000000000002-20000
χ462-22-22-2200002-2-22-22-2002i−2i2i−2i2-200002-2-2200002i−2i2i−2i00000000−2i−2i2i2i000000000000000000-220000
χ472-22-22-2200002-2-22-22-200−2i2i−2i2i2-200002-2-220000−2i2i−2i2i000000002i2i−2i−2i000000000000000000-220000
χ482-22-22-2200002-2-22-22-200−2i2i−2i2i2-200002-2-220000−2i2i−2i2i00000000−2i−2i2i2i0000000000000000002-20000
χ492-22-22-220000-222-2-22-2002i−2i−2i2i2-20000-222-200002i−2i−2i2i000022-2-2000000000000000000002i−2i000000
χ502-22-22-220000-222-2-22-2002i−2i−2i2i2-20000-222-200002i−2i−2i2i0000-2-22200000000000000000000−2i2i000000
χ512-22-22-220000-222-2-22-200−2i2i2i−2i2-20000-222-20000−2i2i2i−2i000022-2-200000000000000000000−2i2i000000
χ522-22-22-220000-222-2-22-200−2i2i2i−2i2-20000-222-20000−2i2i2i−2i0000-2-222000000000000000000002i−2i000000
χ534444-4-4-244-4-44-44-4-2-2-24-4000022-2-222-22-2200-220000000000000000000000000000000000000000
χ544444-4-4-244-4-4-44-44-2-2-2-44000022-2-2222-22-2002-20000000000000000000000000000000000000000
χ554444-4-4-2-4-4444-44-4-2-2-2-4400002222-2-2-22-22002-20000000000000000000000000000000000000000
χ564444-4-4-2-4-444-44-44-2-2-24-400002222-2-22-22-200-220000000000000000000000000000000000000000
χ5744-4-40044-40000004-4-4000000004-40000000000000000002-22-22-22-2000000000000000000000000
χ5844-4-40044-40000004-4-4000000004-4000000000000000000-22-22-22-22000000000000000000000000
χ5944-4-4004-440000004-4-400000000-440000000000000000002-22-2-22-22000000000000000000000000
χ6044-4-4004-440000004-4-400000000-44000000000000000000-22-222-22-2000000000000000000000000
χ614-44-44-4-200004-4-442-22004i−4i4i−4i-220000-222-20000−2i2i−2i2i000000000000000000000000000000000000
χ624-44-44-4-200004-4-442-2200−4i4i−4i4i-220000-222-200002i−2i2i−2i000000000000000000000000000000000000
χ634-44-44-4-20000-444-42-22004i−4i−4i4i-2200002-2-220000−2i2i2i−2i000000000000000000000000000000000000
χ644-44-44-4-20000-444-42-2200−4i4i4i−4i-2200002-2-2200002i−2i−2i2i000000000000000000000000000000000000
χ654-44-4-444000044-4-4-44-4000000-44000044-4-400000000000000000000000000000000000000000000
χ664-44-4-4440000-4-444-44-4000000-440000-4-44400000000000000000000000000000000000000000000
χ674-44-4-44-2000044-4-42-220000002-20000-2-22200000000−2i32i3−2i32i300000000000000000000000000000000
χ684-44-4-44-2000044-4-42-220000002-20000-2-222000000002i3−2i32i3−2i300000000000000000000000000000000
χ694-44-4-44-20000-4-4442-220000002-2000022-2-200000000−2i32i32i3−2i300000000000000000000000000000000
χ704-44-4-44-20000-4-4442-220000002-2000022-2-2000000002i3−2i3−2i32i300000000000000000000000000000000
χ714-4-44004004i−4i0000-4-4400000000004i−4i00000000000000002-2-222i−2i−2i2i000000000000000000000000
χ724-4-44004004i−4i0000-4-4400000000004i−4i0000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ734-4-4400400−4i4i0000-4-440000000000−4i4i00000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ744-4-4400400−4i4i0000-4-440000000000−4i4i0000000000000000-222-22i−2i−2i2i000000000000000000000000
χ7588-8-800-48-8000000-44400000000-4400000000000000000000000000000000000000000000000000
χ7688-8-800-4-88000000-444000000004-400000000000000000000000000000000000000000000000000
χ778-8-8800-4008i−8i000044-40000000000−4i4i000000000000000000000000000000000000000000000000
χ788-8-8800-400−8i8i000044-400000000004i−4i000000000000000000000000000000000000000000000000

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