Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2666 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, prime radical, cosocle | C23×C13 | C24 |
| Fitting | C4×C13×C4⋊C4 | C2 |
| hypercenter | C4×C4⋊C4 | D13 |
| hypocenter | C13 | #2666 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
368 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=g,c^2=g,d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^12272 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2666, C2×#13121015, #16029688, … |
| maximal normal subgroup of | D13×#2666, C2×#13121015, #16029688, … |
| maximal quotient of | #15789528, #15789537, #15789552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 10689);