Finite Group DatabasebetaFinite Group Databasebeta| order | 23534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C41 |
| unambiguous semidirect product | C7⋊(C41⋊D41) |
| unambiguous semidirect product | C41⋊D287 |
| Fitting, socle, derived, Hall | C7×C412 ⋊ C2 |
| Sylow | C412 ⋊ D7 |
| Sylow | C7 ⋊ C41⋊D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C412 | C2 |
| LCS | G ▷ C7×C412 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11767 |
Polycyclic presentation:
2,7,41^2|b^a=b^6,c^a=c^40,d^a=d^405885 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23534, 13);