Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #26044451⋊C2 |
| Fitting, socle, Sylow | C292 ⋊ C2×D7 |
| derived, Hall | #19154637 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #19154637 | C22 |
| Fitting, socle | C292 | C2×D7 |
| LCS | G ▷ #19154637 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 58 |
Polycyclic presentation:
2^2,7,29^2|d^a=d^28,e^a=e^28,c^b=c^6,d^b=e^9,e^b=d^13,d^c=d^20,e^c=e^1682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 43);