Finite Group DatabasebetaFinite Group Databasebeta| order | 23534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C41 |
| unambiguous semidirect product | (C41⋊D41)⋊C7 |
| Fitting, socle, derived, Sylow | C412 ⋊ C2×C7 |
| Hall | C412⋊C7 ⋊ C2 |
| Hall | C41⋊D41 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C412 | C2×C7 |
| LCS | G ▷ C412 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 287 |
Polycyclic presentation:
2,7,41^2|c^a=c^40,d^a=d^40,c^b=c^28d^14,d^b=cd^2134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23534, 7);