Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #26044457⋊C2 |
| unambiguous semidirect product | #26044458⋊C2 |
| unambiguous semidirect product | #26044461⋊C2 |
| Fitting, socle, derived, Sylow | C292 ⋊ C22×C7 |
| Hall | #19154635 ⋊ C22 |
| Hall | D292 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C292 | C22×C7 |
| LCS | G ▷ C292 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 406 |
Polycyclic presentation:
2^2,7,29^2|e^a=e^28,d^b=d^28,d^c=d^16,e^c=e^2464 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 65);