Finite Group Databasebeta

← Group #10691503

Character table — Group #10691503

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order1222223444444666666622444441212121212121212446688881212121212121212242424242424242488884412121212444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111111111111111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111-1-11-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111-1-11-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ9111111111-1-1-1-11111111-1-1111-1-111-1-1-1-1111-1-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−i1-111-1-1ii−i−ii−iii−i−ii−i
χ10111111111-1-1-1-11111111-1-1111-1-111-1-1-1-1111-1-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii1-111-1-1−i−iii−ii−i−iii−ii
χ11111111111-1-1-1-11111111-1-1111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i-11-1-111−i−iiii−iii−i−i−ii
χ12111111111-1-1-1-11111111-1-1111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iii-11-1-111ii−i−i−ii−i−iiii−i
χ13111111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-11-1-111-1-1-1-1-1-111111111-1-1-1-1ii−i−i-11-1-111ii−i−ii−i−i−iii−ii
χ14111111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-11-1-111-1-1-1-1-1-111111111-1-1-1-1−i−iii-11-1-111−i−iii−iiii−i−ii−i
χ15111111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-11-1-1-1-111-1-1-1-11111-1-1-1-11111ii−i−i1-111-1-1−i−iiii−i−i−iiii−i
χ16111111111-1-1-1-11111111-1-1-1-111111-1-1-1-111-11-1-1-1-111-1-1-1-11111-1-1-1-11111−i−iii1-111-1-1ii−i−i−iiii−i−i−ii
χ172222222-2-222222222222-2-200-200-2-22222-2-200-2-20000000000000000000022220000000000-2-2000000
χ182222222-2-222222222222-2-200-200-2-22222-2-200-2-200000000000000000000-2-2-2-2000000000022000000
χ192222222-2-2-2-2-2-222222222200-200-2-2-2-2-2-2-2-20022000000000000000000002i2i−2i−2i0000000000−2i2i000000
χ202222222-2-2-2-2-2-222222222200-200-2-2-2-2-2-2-2-2002200000000000000000000−2i−2i2i2i00000000002i−2i000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-122-2-22-2-2-1-1-1-1-1-1-1-1-2-2-1-1222211111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-122-2-22-2-2-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-21111111111111111000022-1-1-1-1000000000000
χ25222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2222-2-2-1-11111-1-12-21122-2-2-1-1-1-11111-1-1-1-1111100002-2-1-111000000000000
χ26222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2222-2-2-1-11111-1-12-211-2-222-1-1-1-111111111-1-1-1-10000-2211-1-1000000000000
χ27222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222-1-11111-1-1-221122-2-21111-1-1-1-1-1-1-1-111110000-2211-1-1000000000000
χ28222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222-1-11111-1-1-2211-2-2221111-1-1-1-11111-1-1-1-100002-2-1-111000000000000
χ292222-2-222222-2-2-2-2-2-2222-2222-2-2-2-2-222-2-222-222-2000022-2-222-2-2000000000000000000000000000000
χ302222-2-222222-2-2-2-2-2-2222-22-2-2-222-2-222-2-2222-22-20000-2-222-2-222000000000000000000000000000000
χ312222-2-2222-2-222-2-2-2-22222-222-222-2-2-2-22222-2-2-22000022-2-2-2-222000000000000000000000000000000
χ322222-2-2222-2-222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222222-220000-2-22222-2-2000000000000000000000000000000
χ332222-2-22-2-222-2-2-2-2-2-22222-2002002222-2-2-2-200-220000000000000000000000000000000000002i−2i2i−2i00
χ342222-2-22-2-222-2-2-2-2-2-22222-2002002222-2-2-2-200-22000000000000000000000000000000000000−2i2i−2i2i00
χ352222-2-22-2-2-2-222-2-2-2-2222-220020022-2-222-2-2002-20000000000000000000000000000000000002-2-2200
χ362222-2-22-2-2-2-222-2-2-2-2222-220020022-2-222-2-2002-2000000000000000000000000000000000000-222-200
χ372222-2-2-12222-2-21111-1-1-1-2222-2-2-211-1-111-1-1-22-110000-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-12222-2-21111-1-1-1-2222-2-2-211-1-111-1-1-22-110000-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-12222-2-21111-1-1-1-22-2-2-22211-1-111-1-12-2-11000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-12222-2-21111-1-1-1-22-2-2-22211-1-111-1-12-2-11000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-122-2-2221111-1-1-12-222-2221111-1-1-1-1-2-21-10000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ422222-2-2-122-2-2221111-1-1-12-222-2221111-1-1-1-1-2-21-10000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ432222-2-2-122-2-2221111-1-1-12-2-2-2-2-2-21111-1-1-1-1221-1000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ442222-2-2-122-2-2221111-1-1-12-2-2-2-2-2-21111-1-1-1-1221-1000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ452-22-22-22002i−2i2i−2i22-2-2-22-20000000002i−2i2i−2i0000002−2−i2i2000000002−22−2−i2i2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000001+i−1−i1−i−1+i00000000
χ462-22-22-22002i−2i2i−2i22-2-2-22-20000000002i−2i2i−2i0000002−2−i2i2000000002−22−2−i2i2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−1−i1+i−1+i1−i00000000
χ472-22-22-22002i−2i2i−2i22-2-2-22-20000000002i−2i2i−2i000000−22i2−i200000000−22−22i2−i2i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−1−i1+i−1+i1−i00000000
χ482-22-22-22002i−2i2i−2i22-2-2-22-20000000002i−2i2i−2i000000−22i2−i200000000−22−22i2−i2i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000001+i−1−i1−i−1+i00000000
χ492-22-22-2200−2i2i−2i2i22-2-2-22-2000000000−2i2i−2i2i0000002−2i2−i2000000002−22−2i2−i2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000001−i−1+i1+i−1−i00000000
χ502-22-22-2200−2i2i−2i2i22-2-2-22-2000000000−2i2i−2i2i0000002−2i2−i2000000002−22−2i2−i2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−1+i1−i−1−i1+i00000000
χ512-22-22-2200−2i2i−2i2i22-2-2-22-2000000000−2i2i−2i2i000000−22−i2i200000000−22−22−i2i2−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−1+i1−i−1−i1+i00000000
χ522-22-22-2200−2i2i−2i2i22-2-2-22-2000000000−2i2i−2i2i000000−22−i2i200000000−22−22−i2i2−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000001−i−1+i1+i−1−i00000000
χ53444444-2-4-44444-2-2-2-2-2-2-2-4-400-40022-2-2-2-2220022000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-2-2-2-24400-4002222222200-2-2000000000000000000000000000000000000000000
χ554444-4-4-2-4-444-4-42222-2-2-24-400400-2-2-2-22222002-2000000000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4442222-2-2-2-4400400-2-222-2-22200-22000000000000000000000000000000000000000000
χ574-44-44-4-2004i−4i4i−4i-2-2222-22000000000−2i2i−2i2i00000022−22−2i22i200000000−22−22i2−i2i2−i20000000000000000000000
χ584-44-44-4-2004i−4i4i−4i-2-2222-22000000000−2i2i−2i2i000000−22222i2−2i2000000002−22−2−i2i2−i2i20000000000000000000000
χ594-44-44-4-200−4i4i−4i4i-2-2222-220000000002i−2i2i−2i00000022−222i2−2i200000000−22−22−i2i2−i2i20000000000000000000000
χ604-44-44-4-200−4i4i−4i4i-2-2222-220000000002i−2i2i−2i000000−2222−2i22i2000000002−22−2i2−i2i2−i20000000000000000000000
χ614-44-4-444004i−4i−4i4i-4-444-44-40000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ624-44-4-44400−4i4i4i−4i-4-444-44-4000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ634-44-4-44-2004i−4i−4i4i22-2-22-22000000000−2i2i2i−2i000000000000000000i6−i6−i6i66−6−660000000000000000000000
χ644-44-4-44-2004i−4i−4i4i22-2-22-22000000000−2i2i2i−2i000000000000000000−i6i6i6−i6−666−60000000000000000000000
χ654-44-4-44-200−4i4i4i−4i22-2-22-220000000002i−2i−2i2i000000000000000000i6−i6−i6i6−666−60000000000000000000000
χ664-44-4-44-200−4i4i4i−4i22-2-22-220000000002i−2i−2i2i000000000000000000−i6i6i6−i66−6−660000000000000000000000
χ674-4-440044-400000000-4-44000004i−4i0000004-4000000000000004i−4i000000000000000000000000000000
χ684-4-440044-400000000-4-4400000−4i4i0000004-400000000000000−4i4i000000000000000000000000000000
χ694-4-44004-4400000000-4-44004i−4i000000000-44000000004i−4i000000000000000000000000000000000000
χ704-4-44004-4400000000-4-4400−4i4i000000000-4400000000−4i4i000000000000000000000000000000000000
χ714-4-4400-24-40000−2i32i3−2i32i322-2000004i−4i−2i32i30000-2200000000000023−23−2i2i000000000000000000000000000000
χ724-4-4400-24-40000−2i32i3−2i32i322-200000−4i4i−2i32i30000-22000000000000−23232i−2i000000000000000000000000000000
χ734-4-4400-24-400002i3−2i32i3−2i322-2000004i−4i2i3−2i30000-22000000000000−2323−2i2i000000000000000000000000000000
χ744-4-4400-24-400002i3−2i32i3−2i322-200000−4i4i2i3−2i30000-2200000000000023−232i−2i000000000000000000000000000000
χ754-4-4400-2-440000−2i32i3−2i32i322-2004i−4i0002i3−2i300002-200000000−2i2i23−230000000000000000000000000000000000
χ764-4-4400-2-440000−2i32i3−2i32i322-200−4i4i0002i3−2i300002-2000000002i−2i−23230000000000000000000000000000000000
χ774-4-4400-2-4400002i3−2i32i3−2i322-2004i−4i000−2i32i300002-200000000−2i2i−23230000000000000000000000000000000000
χ784-4-4400-2-4400002i3−2i32i3−2i322-200−4i4i000−2i32i300002-2000000002i−2i23−230000000000000000000000000000000000
χ7988-8-800800000000008-8-80000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-4000000−4i34i34i3−4i3-4440000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-40000004i3−4i3−4i34i3-4440000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.