Finite Group DatabasebetaFinite Group Databasebeta| order | 23534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C412 ⋊ D7 |
| derived, Hall | C412⋊C7 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C412⋊C7 | C2 |
| Fitting, socle | C412 | D7 |
| LCS | G ▷ C412⋊C7 | |
| UCS | C1 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 287 |
Polycyclic presentation:
2,7,41^2|b^a=b^6,d^a=c^3d^40,c^b=c^9d^26,d^b=c^8d^5185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23534, 6);