Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#385 ⋊ C2 |
| Sylow | C13 ⋊ #2638 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C13×#385 | C2 |
| prime radical | C22×C22⋊D13 | C22 |
| hypercenter | #385 | D13 |
| hypocenter | C13 | #2638 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #385 | |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|c^2=e,d^2=ef,b^a=be,c^a=cf,h^a=h^12,c^b=cg,d^c=de200 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2638, C2×#13120757, #16029336, … |
| maximal normal subgroup of | D13×#2638, C2×#13120757, #16029336, … |
| maximal quotient of | #15789409, #15789411, #15789428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 10431);