Finite Group Databasebeta

← Group #10691653

Character table — Group #10691653

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222222223446666666444444466661212121244888812121212121212121212242424242424242444444412121212444444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ9111111-1-1-1-111111-1-1-1-111-111-1-1-111-1-111-1-11-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−iii−i−ii−iii−i−ii−iii−i−i11-1-11-1
χ10111111-1-1-1-111111-1-1-1-111-111-1-1-111-1-111-1-11-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i−i−iiii−iii−i−i−ii−i−iii-1-111-11
χ11111111-1-1-1-111111-1-1-1-111-111-1-1-111-1-111-1-11-1−i−iii1-11111-1-1-1-1−i−i−i−iiiiiii−i−i−ii−i−iiii−iii−i−i-1-111-11
χ12111111-1-1-1-111111-1-1-1-111-111-1-1-111-1-111-1-11-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−i−iii−ii−i−iii−ii−i−iii11-1-11-1
χ13111111-1-1-1-111111-1-1-1-111-1-1-111-111-1-111-1-1-11ii−i−i1-1-1-1-1-11111iiii−i−i−i−iii−i−i−ii−i−iiii−i−i−iii11-1-1-11
χ14111111-1-1-1-111111-1-1-1-111-1-1-111-111-1-111-1-1-11ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−i−iii−ii−i−iii−iiii−i−i-1-1111-1
χ15111111-1-1-1-111111-1-1-1-111-1-1-111-111-1-111-1-1-11−i−iii1-1-1-1-1-11111−i−i−i−iiiiiii−i−ii−iii−i−ii−i−i−iii-1-1111-1
χ16111111-1-1-1-111111-1-1-1-111-1-1-111-111-1-111-1-1-11−i−iii1-1-1-1-1-11111−i−i−i−iiiii−i−iiii−iii−i−i−iiii−i−i11-1-1-11
χ1722222222222-2-22222222-2-20000-22222-2-2-2-2000000-2-200000000000000002222000000-2-20000000000
χ1822222222222-2-22222222-2-20000-22222-2-2-2-2000000-2-20000000000000000-2-2-2-2000000220000000000
χ192222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ202222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ212222222222-122-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ222222222222-122-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ23222222-2-2-2-22-2-222-2-2-2-22-220000222-2-2-2-222000000-2200000000000000002i2i−2i−2i000000−2i2i0000000000
χ24222222-2-2-2-22-2-222-2-2-2-22-220000222-2-2-2-222000000-220000000000000000−2i−2i2i2i0000002i−2i0000000000
χ25222222-2-2-2-2-122-1-11111-12-222-2-2-2-1-111-1-1112-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii00002i−2i−i−iii000000000000
χ26222222-2-2-2-2-122-1-11111-12-222-2-2-2-1-111-1-1112-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i0000−2i2iii−i−i000000000000
χ27222222-2-2-2-2-122-1-11111-12-2-2-222-2-1-111-1-111-222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii0000−2i2iii−i−i000000000000
χ28222222-2-2-2-2-122-1-11111-12-2-2-222-2-1-111-1-111-22−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i00002i−2i−i−iii000000000000
χ292222-2-222-2-22222222222-2-222-2-22-2-2-2-22222-220000-2-222-2-222-2-2000000000000000000000000000000
χ302222-2-222-2-22222222222-2-2-2-2222-2-2-2-222222-20000-2-2-2-222-2-222000000000000000000000000000000
χ312222-2-222-2-22-2-22222222220000-2-2-2-2-2-2-2-2-20000002200000000000000000000000000002i−2i2i−2i000000
χ322222-2-222-2-22-2-22222222220000-2-2-2-2-2-2-2-2-2000000220000000000000000000000000000−2i2i−2i2i000000
χ332222-2-222-2-2-122-1-1-1-1-1-1-1-2-222-2-221111-1-1-1-1-22000011-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ342222-2-222-2-2-122-1-1-1-1-1-1-1-2-222-2-221111-1-1-1-1-22000011-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ352222-2-222-2-2-122-1-1-1-1-1-1-1-2-2-2-22221111-1-1-1-12-200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ362222-2-222-2-2-122-1-1-1-1-1-1-1-2-2-2-22221111-1-1-1-12-200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ372222-2-2-2-22222222-2-2-2-22-222222-2-2-22222-2-2-2-20000-2222-2-2-2-222000000000000000000000000000000
χ382222-2-2-2-22222222-2-2-2-22-22-2-2-2-2-2-2-22222-2-2220000-22-2-22222-2-2000000000000000000000000000000
χ392222-2-2-2-2222-2-222-2-2-2-222-200002-2-222-2-2220000002-200000000000000000000000000002-2-22000000
χ402222-2-2-2-2222-2-222-2-2-2-222-200002-2-222-2-2220000002-20000000000000000000000000000-222-2000000
χ412222-2-2-2-222-122-1-11111-1-222222-211-1-1-1-111-2-200001-1-1-11111-1-133−3−3−3−3330000003−3−33000000000000
χ422222-2-2-2-222-122-1-11111-1-222222-211-1-1-1-111-2-200001-1-1-11111-1-1−3−33333−3−3000000−333−3000000000000
χ432222-2-2-2-222-122-1-11111-1-22-2-2-2-2-211-1-1-1-1112200001-111-1-1-1-11133−3−3−3−333000000−333−3000000000000
χ442222-2-2-2-222-122-1-11111-1-22-2-2-2-2-211-1-1-1-1112200001-111-1-1-1-111−3−33333−3−30000003−3−33000000000000
χ452-22-22-22-2-222002-222-2-2-200000002-22-20000002−22−200000000002−22−22−22−22i−2i2i−2i000000000000−i2i2−i2i200
χ462-22-22-22-2-222002-222-2-2-200000002-22-20000002−22−200000000002−22−22−22−2−2i2i−2i2i000000000000i2−i2i2−i200
χ472-22-22-22-2-222002-222-2-2-200000002-22-2000000−22−220000000000−22−22−22−222i−2i2i−2i000000000000i2−i2i2−i200
χ482-22-22-22-2-222002-222-2-2-200000002-22-2000000−22−220000000000−22−22−22−22−2i2i−2i2i000000000000−i2i2−i2i200
χ492-22-22-2-222-22002-2-2-222-200000002-2-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i22-2-22000000000000−i2i2i2−i200
χ502-22-22-2-222-22002-2-2-222-200000002-2-22000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2-222-2000000000000i2−i2−i2i200
χ512-22-22-2-222-22002-2-2-222-200000002-2-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i22-2-22000000000000i2−i2−i2i200
χ522-22-22-2-222-22002-2-2-222-200000002-2-22000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2-222-2000000000000−i2i2i2−i200
χ534444444444-2-4-4-2-2-2-2-2-2-2-4-40000-4-2-2-2-222220000002200000000000000000000000000000000000000
χ54444444-4-4-4-4-2-4-4-2-22222-2-4400004-2-22222-2-20000002-200000000000000000000000000000000000000
χ554444-4-444-4-4-2-4-4-2-2-2-2-2-2-2440000-422222222000000-2-200000000000000000000000000000000000000
χ564444-4-4-4-444-2-4-4-2-22222-24-40000422-2-222-2-2000000-2200000000000000000000000000000000000000
χ574-44-44-44-4-44-200-22-2-22220000000-22-2200000022−2222−220000000000−22−22−22−220000000000000000000000
χ584-44-44-44-4-44-200-22-2-22220000000-22-22000000−2222−222200000000002−22−22−22−20000000000000000000000
χ594-44-44-4-444-4-200-2222-2-220000000-222-2000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ604-44-44-4-444-4-200-2222-2-220000000-222-20000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ614-44-4-444-44-44004-444-4-4-40000000-44-4400000000000000000000000000000000000000000000000000
χ624-44-4-444-44-4-200-22-2-222200000002-22-200000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ634-44-4-444-44-4-200-22-2-222200000002-22-200000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ644-44-4-44-44-444004-4-4-444-40000000-444-400000000000000000000000000000000000000000000000000
χ654-44-4-44-44-44-200-2222-2-2200000002-2-22000000000000000000006−6−66−666−60000000000000000000000
χ664-44-4-44-44-44-200-2222-2-2200000002-2-2200000000000000000000−666−66−6−660000000000000000000000
χ674-4-4400000044-4-4-40000400004-4000004-400000000000000004-4000000000000000000000000000000
χ684-4-4400000044-4-4-4000040000-44000004-40000000000000000-44000000000000000000000000000000
χ694-4-440000004-44-4-400004004-40000000-4400000000004-4000000000000000000000000000000000000
χ704-4-440000004-44-4-40000400-440000000-440000000000-44000000000000000000000000000000000000
χ714-4-44000000-24-422−2i32i3−2i32i3-200004-400000-22−2i32i30000000000−2i32i300-22000000000000000000000000000000
χ724-4-44000000-24-422−2i32i3−2i32i3-20000-4400000-22−2i32i300000000002i3−2i3002-2000000000000000000000000000000
χ734-4-44000000-24-4222i3−2i32i3−2i3-200004-400000-222i3−2i300000000002i3−2i300-22000000000000000000000000000000
χ744-4-44000000-24-4222i3−2i32i3−2i3-20000-4400000-222i3−2i30000000000−2i32i3002-2000000000000000000000000000000
χ754-4-44000000-2-4422−2i32i3−2i32i3-2004-400000002-22i3−2i300000000-2200−2i32i300000000000000000000000000000000
χ764-4-44000000-2-4422−2i32i3−2i32i3-200-4400000002-22i3−2i3000000002-2002i3−2i300000000000000000000000000000000
χ774-4-44000000-2-44222i3−2i32i3−2i3-2004-400000002-2−2i32i300000000-22002i3−2i300000000000000000000000000000000
χ784-4-44000000-2-44222i3−2i32i3−2i3-200-4400000002-2−2i32i3000000002-200−2i32i300000000000000000000000000000000
χ7988-8-8000000800-880000-80000000000000000000000000000000000000000000000000000000000000
χ8088-8-8000000-4004-4−4i34i34i3−4i340000000000000000000000000000000000000000000000000000000000000
χ8188-8-8000000-4004-44i3−4i3−4i34i340000000000000000000000000000000000000000000000000000000000000

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