Finite Group Databasebeta

← Group #10691671

Character table — Group #10691671

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222222344446662446666121212121212244468888122424242424242424888888882466612121212124444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11-1-1111-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111-111-1-1-111-1-1-1-111-1-111
χ811111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1111111-1-111-1-1
χ9111111-1-11-1-1-1-1111-11111-1-1-1-1-1-11111-1-1-111-1-111111-1-1-1-1ii−i−iii−i−i1-11111-1-1-1-1ii−i−ii−ii−ii−i
χ10111111-1-11-1-1-1-1111-11111-1-1-1-1-1-11111-1-1-111-1-111111-1-1-1-1−i−iii−i−iii1-11111-1-1-1-1−i−iii−ii−ii−ii
χ11111111-1-11-1-1-1-1111-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-11111ii−i−iii−i−i-111-1-11-1-111−i−iiii−ii−i−ii
χ12111111-1-11-1-1-1-1111-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-11111−i−iii−i−iii-111-1-11-1-111ii−i−i−ii−iii−i
χ13111111-1-11-1-1-1-1111-11111-1-1-1-1-1-111-1-111-111-1-111111-1-1-1-1ii−i−i−i−iii-11-1-1-1-11111ii−i−ii−i−ii−ii
χ14111111-1-11-1-1-1-1111-11111-1-1-1-1-1-111-1-111-111-1-111111-1-1-1-1−i−iiiii−i−i-11-1-1-1-11111−i−iii−iii−ii−i
χ15111111-1-11-1-1-1-1111-11111-1-1-1-1-1-111-1-111-1-1-1111-1-1-1-11111ii−i−i−i−iii1-1-111-111-1-1−i−iiii−i−iii−i
χ16111111-1-11-1-1-1-1111-11111-1-1-1-1-1-111-1-111-1-1-1111-1-1-1-11111−i−iiiii−i−i1-1-111-111-1-1ii−i−i−iii−i−ii
χ17222222222-2-2-2-22222-2-22222-2-2-2-2-2-2000020000-2000000002i2i−2i−2i000000000000000000−2i2i0000
χ18222222222-2-2-2-22222-2-22222-2-2-2-2-2-2000020000-200000000−2i−2i2i2i0000000000000000002i−2i0000
χ1922222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ2022222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-11111111100000000-2-2-111-1-1-1110000000000
χ2122222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ2222222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-11111111100000000221-1-1111-1-10000000000
χ23222222-2-222222222-2-2-222-2-22222-2-20000-20000-2000000002222000000000000000000-2-20000
χ24222222-2-222222222-2-2-222-2-22222-2-20000-20000-200000000-2-2-2-2000000000000000000220000
χ25222222-2-2-1-2-2-2-2-1-1-1-222-1-1111111-1-122-2-2122-2-2-1-1-1-1-11111000000002-2-1-1-1-111110000000000
χ26222222-2-2-1-2-2-2-2-1-1-1-222-1-1111111-1-122-2-21-2-222-11111-1-1-1-100000000-22-111-111-1-10000000000
χ27222222-2-2-1-2-2-2-2-1-1-1-222-1-1111111-1-1-2-222122-2-2-1-1-1-1-1111100000000-221111-1-1-1-10000000000
χ28222222-2-2-1-2-2-2-2-1-1-1-222-1-1111111-1-1-2-2221-2-222-11111-1-1-1-1000000002-21-1-11-1-1110000000000
χ292222-2-222222-2-2222-2-22-2-22222-2-2222-22-2-20000-2000000000000000000200-22-2000000000000
χ302222-2-222222-2-2222-2-22-2-22222-2-222-22-22-20000-2000000000000000000-2002-22000000000000
χ312222-2-2222-2-222222-22-2-2-222-2-222-2-20000-20000200000000000022220000000000000000-2-200
χ322222-2-2222-2-222222-22-2-2-222-2-222-2-20000-200002000000000000-2-2-2-200000000000000002200
χ332222-2-222-122-2-2-1-1-1-2-2211-1-1-1-111-1-12-22-2100001−i3−i3i3i3−i3−i3i3i30000000000-1−i3i31-11−i3i30000000000
χ342222-2-222-122-2-2-1-1-1-2-2211-1-1-1-111-1-12-22-2100001i3i3−i3−i3i3i3−i3−i30000000000-1i3−i31-11i3−i30000000000
χ352222-2-222-122-2-2-1-1-1-2-2211-1-1-1-111-1-1-22-22100001−i3−i3i3i3−i3−i3i3i300000000001i3−i3-11-1i3−i30000000000
χ362222-2-222-122-2-2-1-1-1-2-2211-1-1-1-111-1-1-22-22100001i3i3−i3−i3i3i3−i3−i300000000001−i3i3-11-1−i3i30000000000
χ372222-2-2-2-2222-2-222222-2-2-2-2-222-2-2-2-200002000020000000000002i2i−2i−2i0000000000000000−2i2i00
χ382222-2-2-2-2222-2-222222-2-2-2-2-222-2-2-2-20000200002000000000000−2i−2i2i2i00000000000000002i−2i00
χ392222-2-2-2-22-2-2222222-22-2-2-2-2-2-222222-2-2220000-2000000000000000000200-2-22000000000000
χ402222-2-2-2-22-2-2222222-22-2-2-2-2-2-22222-222-220000-2000000000000000000-20022-2000000000000
χ412222-2-2-2-2-1-2-222-1-1-12-22111111-1-1-1-12-2-22-100001−i3−i3i3i3i3i3−i3−i30000000000-1−i3i311-1i3−i30000000000
χ422222-2-2-2-2-1-2-222-1-1-12-22111111-1-1-1-12-2-22-100001i3i3−i3−i3−i3−i3i3i30000000000-1i3−i311-1−i3i30000000000
χ432222-2-2-2-2-1-2-222-1-1-12-22111111-1-1-1-1-222-2-100001−i3−i3i3i3i3i3−i3−i300000000001i3−i3-1-11−i3i30000000000
χ442222-2-2-2-2-1-2-222-1-1-12-22111111-1-1-1-1-222-2-100001i3i3−i3−i3−i3−i3i3i300000000001−i3i3-1-11i3−i30000000000
χ4522-2-22-20022i−2i2i−2i2-2-20002-2002i−2i2i−2i00000002−2−i2i202−22−2−i2i2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000001+i−1−i1−i−1+i000000
χ4622-2-22-20022i−2i2i−2i2-2-20002-2002i−2i2i−2i00000002−2−i2i202−22−2−i2i2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−1−i1+i−1+i1−i000000
χ4722-2-22-20022i−2i2i−2i2-2-20002-2002i−2i2i−2i0000000−22i2−i20−22−22i2−i2i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−1−i1+i−1+i1−i000000
χ4822-2-22-20022i−2i2i−2i2-2-20002-2002i−2i2i−2i0000000−22i2−i20−22−22i2−i2i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000001+i−1−i1−i−1+i000000
χ4922-2-22-2002−2i2i−2i2i2-2-20002-200−2i2i−2i2i00000002−2i2−i202−22−2i2−i2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000001−i−1+i1+i−1−i000000
χ5022-2-22-2002−2i2i−2i2i2-2-20002-200−2i2i−2i2i00000002−2i2−i202−22−2i2−i2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−1+i1−i−1−i1+i000000
χ5122-2-22-2002−2i2i−2i2i2-2-20002-200−2i2i−2i2i0000000−22−i2i20−22−22−i2i2−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000−1+i1−i−1−i1+i000000
χ5222-2-22-2002−2i2i−2i2i2-2-20002-200−2i2i−2i2i0000000−22−i2i20−22−22−i2i2−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000001−i−1+i1+i−1−i000000
χ5344444444-2-4-4-4-4-2-2-24-4-4-2-2-2-22222220000-200002000000000000000000000000000000000000
χ54444444-4-4-24444-2-2-2-4-4-4-2-222-2-2-2-2220000200002000000000000000000000000000000000000
χ554444-4-444-2-4-444-2-2-2-44-422-2-222-2-222000020000-2000000000000000000000000000000000000
χ564444-4-4-4-4-244-4-4-2-2-244-42222-2-222220000-20000-2000000000000000000000000000000000000
χ5744-4-44-400-24i−4i4i−4i-222000-2200−2i2i−2i2i000000022−22−2i22i20−22−22i2−i2i2−i20000000000000000000000000000
χ5844-4-44-400-24i−4i4i−4i-222000-2200−2i2i−2i2i0000000−22222i2−2i202−22−2−i2i2−i2i20000000000000000000000000000
χ5944-4-44-400-2−4i4i−4i4i-222000-22002i−2i2i−2i000000022−222i2−2i20−22−22−i2i2−i2i20000000000000000000000000000
χ6044-4-44-400-2−4i4i−4i4i-222000-22002i−2i2i−2i0000000−2222−2i22i202−22−2i2−i2i2−i20000000000000000000000000000
χ6144-4-4-440044i−4i−4i4i4-4-4000-44004i−4i−4i4i000000000000000000000000000000000000000000000000
χ6244-4-4-44004−4i4i4i−4i4-4-4000-4400−4i4i4i−4i000000000000000000000000000000000000000000000000
χ6344-4-4-4400-24i−4i−4i4i-2220002-200−2i2i2i−2i000000000000i6−i6−i6i66−6−660000000000000000000000000000
χ6444-4-4-4400-24i−4i−4i4i-2220002-200−2i2i2i−2i000000000000−i6i6i6−i6−666−60000000000000000000000000000
χ6544-4-4-4400-2−4i4i4i−4i-2220002-2002i−2i−2i2i000000000000i6−i6−i6i6−666−60000000000000000000000000000
χ6644-4-4-4400-2−4i4i4i−4i-2220002-2002i−2i−2i2i000000000000−i6i6i6−i66−6−660000000000000000000000000000
χ674-44-4004-440000-44-4000004-40000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ684-44-4004-440000-44-4000004-400000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ694-44-400-4440000-44-400000-44000000000000000000000000000022−22−222200000000000000000000
χ704-44-400-4440000-44-400000-440000000000000000000000000000−222222−2200000000000000000000
χ718-88-8008-8-400004-4400000-440000000000000000000000000000000000000000000000000000
χ728-88-800-88-400004-44000004-40000000000000000000000000000000000000000000000000000
χ738-8-88000080000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-880000-4000044-400000000000−4i34i30000000000000000000000000000000000000000000000
χ758-8-880000-4000044-4000000000004i3−4i30000000000000000000000000000000000000000000000

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