Finite Group Databasebeta

← Group #10883507

Character table — Group #10883507

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order12222234444444466644661212121212121212888844448888121212121212121212128888888824242424242424242244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1
χ91111111-1-1-1-11111111-1-111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-111-1-111-1-11-1-1-1111-11-1
χ101111111-1-1-1-11111111-1-111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-11-1-111-1-111-11-1-111-11-11
χ111111111-1-1-1-11111111-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1111-1-1-1-1111-111-1-11-1-11
χ121111111-1-1-1-11111111-1-111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111-1-1-11111-1-1-1111-1-1-111-1
χ131111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11-111-1-111-1-1-1111-1-1-11-11
χ141111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-11-1-111-1-1111-111-1-11-11-1
χ151111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1111-1-1-1-111-11-1-111-111-1
χ161111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-11-1-1-11111-1-11-1-1-1111-1-11
χ1722222222222-2-2-2-2222-2-2222222-2-2-2-2000000002i−2i2i−2i-2-200000000000000002i−2i2i−2i00000000000000
χ1822222222222-2-2-2-2222-2-2222222-2-2-2-200000000−2i2i−2i2i-2-20000000000000000−2i2i−2i2i00000000000000
χ192222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002i−2i−2i2i2200000000000000002i−2i−2i2i00000000000000
χ202222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000−2i2i2i−2i220000000000000000−2i2i2i−2i00000000000000
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-100002222-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-22222-1-111111111000000-2-2-1-1-1-111110000000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-111111111000000221111-1-1-1-10000000000
χ25222222-12222-2-2-2-2-1-1-1-2-2-1-1-1-1-1-11111000000002i−2i2i−2i11−i3−i3i3i3−i3−i3i3i300000000−ii−ii3−33−30000000000
χ26222222-12222-2-2-2-2-1-1-1-2-2-1-1-1-1-1-11111000000002i−2i2i−2i11i3i3−i3−i3i3i3−i3−i300000000−ii−ii−33−330000000000
χ27222222-12222-2-2-2-2-1-1-1-2-2-1-1-1-1-1-1111100000000−2i2i−2i2i11−i3−i3i3i3−i3−i3i3i300000000i−ii−i−33−330000000000
χ28222222-12222-2-2-2-2-1-1-1-2-2-1-1-1-1-1-1111100000000−2i2i−2i2i11i3i3−i3−i3i3i3−i3−i300000000i−ii−i3−33−30000000000
χ29222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-1000022-2-222-2-211-1-1-1-111110000002-2-1-111-1-1110000000000
χ30222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-1000022-2-2-2-22211-1-1-1-11111000000-2211-1-111-1-10000000000
χ31222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-10000-2-22222-2-2111111-1-1-1-1000000-22-1-11111-1-10000000000
χ32222222-1-2-2-2-22222-1-1-1-2-2-1-11111-1-1-1-10000-2-222-2-222111111-1-1-1-10000002-211-1-1-1-1110000000000
χ33222222-1-2-2-2-2-2-2-2-2-1-1-122-1-111111111000000002i−2i−2i2i-1-1−i3−i3i3i3i3i3−i3−i300000000−iii−i3−3−330000000000
χ34222222-1-2-2-2-2-2-2-2-2-1-1-122-1-111111111000000002i−2i−2i2i-1-1i3i3−i3−i3−i3−i3i3i300000000−iii−i−333−30000000000
χ35222222-1-2-2-2-2-2-2-2-2-1-1-122-1-11111111100000000−2i2i2i−2i-1-1−i3−i3i3i3i3i3−i3−i300000000i−i−ii−333−30000000000
χ36222222-1-2-2-2-2-2-2-2-2-1-1-122-1-11111111100000000−2i2i2i−2i-1-1i3i3−i3−i3−i3−i3i3i300000000i−i−ii3−3−330000000000
χ372222-2-2222-2-22-2-222222-2-2-222-2-22-22-20000000000002-2000000000000000000000000220000-2-200
χ382222-2-2222-2-22-2-222222-2-2-222-2-22-22-20000000000002-2000000000000000000000000-2-200002200
χ392222-2-2222-2-2-222-2222-22-2-222-2-2-22-22222200000000-220000000022-2-2-2-200000000000000000000
χ402222-2-2222-2-2-222-2222-22-2-222-2-2-22-22-2-2-2-200000000-2200000000-2-2222200000000000000000000
χ412222-2-22-2-2222-2-22222-22-2-2-2-2222-22-2000000000000-220000000000000000000000002-20000-2200
χ422222-2-22-2-2222-2-22222-22-2-2-2-2222-22-2000000000000-22000000000000000000000000-2200002-200
χ432222-2-22-2-222-222-22222-2-2-2-2-222-22-222222000000002-200000000-2-222-2-200000000000000000000
χ442222-2-22-2-222-222-22222-2-2-2-2-222-22-22-2-2-2-2000000002-20000000022-2-22200000000000000000000
χ452-2-222-22000022-2-2-22-2002-20000-222-22i2i−2i−2i2i−2i000000002i−2i2i−2i000000002i−2i000000000000002-20000
χ462-2-222-22000022-2-2-22-2002-20000-222-22i2i−2i−2i−2i2i00000000−2i2i−2i2i000000002i−2i00000000000000-220000
χ472-2-222-22000022-2-2-22-2002-20000-222-2−2i−2i2i2i2i−2i000000002i−2i2i−2i00000000−2i2i00000000000000-220000
χ482-2-222-22000022-2-2-22-2002-20000-222-2−2i−2i2i2i−2i2i00000000−2i2i−2i2i00000000−2i2i000000000000002-20000
χ492-2-22-2220000-22-22-22-200-22000022-2-22i2i−2i−2i002-200000000002-22-20000−2i2i0000000000002i−2i000000
χ502-2-22-2220000-22-22-22-200-22000022-2-22i2i−2i−2i00-220000000000-22-220000−2i2i000000000000−2i2i000000
χ512-2-22-2220000-22-22-22-200-22000022-2-2−2i−2i2i2i002-200000000002-22-200002i−2i000000000000−2i2i000000
χ522-2-22-2220000-22-22-22-200-22000022-2-2−2i−2i2i2i00-220000000000-22-2200002i−2i0000000000002i−2i000000
χ534444-4-4-244-4-44-4-44-2-2-24-422-2-222-22-22000000000000-220000000000000000000000000000000000
χ544444-4-4-244-4-4-444-4-2-2-2-4422-2-2222-22-20000000000002-20000000000000000000000000000000000
χ554444-4-4-2-4-4444-4-44-2-2-2-442222-2-2-22-220000000000002-20000000000000000000000000000000000
χ564444-4-4-2-4-444-444-4-2-2-24-42222-2-22-22-2000000000000-220000000000000000000000000000000000
χ5744-4-40044-40000004-4-400004-400000022−2222−2200000000000000000022−22000000000000000000000000
χ5844-4-40044-40000004-4-400004-4000000−2222−2222000000000000000000−2222000000000000000000000000
χ5944-4-4004-440000004-4-40000-4400000022−2222−22000000000000000000−2222000000000000000000000000
χ6044-4-4004-440000004-4-40000-44000000−2222−222200000000000000000022−22000000000000000000000000
χ614-44-4004004i−4i0000-4-440000004i−4i0000−2i22i22i2−2i20000000000000000000022−220000000000000000000000
χ624-44-4004004i−4i0000-4-440000004i−4i00002i2−2i2−2i22i200000000000000000000−22220000000000000000000000
χ634-44-400400−4i4i0000-4-44000000−4i4i0000−2i22i22i2−2i200000000000000000000−22220000000000000000000000
χ644-44-400400−4i4i0000-4-44000000−4i4i00002i2−2i2−2i22i20000000000000000000022−220000000000000000000000
χ654-4-444-440000-4-444-44-4004-400004-4-44000000000000000000000000000000000000000000000000
χ664-4-444-4-2000044-4-42-2200-2200002-2-2200004i−4i00000000−2i2i−2i2i000000000000000000000000000000
χ674-4-444-4-2000044-4-42-2200-2200002-2-220000−4i4i000000002i−2i2i−2i000000000000000000000000000000
χ684-4-444-4-20000-4-4442-2200-220000-222-20000000000000023−23−2323000000000000000000000000000000
χ694-4-444-4-20000-4-4442-2200-220000-222-200000000000000−232323−23000000000000000000000000000000
χ704-4-44-44400004-44-4-44-400-440000-4-444000000000000000000000000000000000000000000000000
χ714-4-44-44-200004-44-42-22002-2000022-2-2000000000000000000−2i32i32i3−2i300000000000000000000000000
χ724-4-44-44-200004-44-42-22002-2000022-2-20000000000000000002i3−2i3−2i32i300000000000000000000000000
χ734-4-44-44-20000-44-442-22002-20000-2-2220000004-40000000000-22-2200000000000000000000000000
χ744-4-44-44-20000-44-442-22002-20000-2-222000000-4400000000002-22-200000000000000000000000000
χ7588-8-800-48-8000000-4440000-44000000000000000000000000000000000000000000000000000000
χ7688-8-800-4-88000000-44400004-4000000000000000000000000000000000000000000000000000000
χ778-88-800-4008i−8i000044-4000000−4i4i0000000000000000000000000000000000000000000000000000
χ788-88-800-400−8i8i000044-40000004i−4i0000000000000000000000000000000000000000000000000000

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