Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C292 ⋊ C4×C7 |
| Hall | C29×C29⋊C7 ⋊ C4 |
| Hall | #16809859 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C292 | C4×C7 |
| prime radical | D29×C29⋊C7 | C2 |
| cosocle | C29×D29 | C2×C7 |
| LCS | G ▷ C292 | |
| UCS | C1 | |
25 conjugacy classes of subgroups.
| transitive degree | μt(G) = 812 |
Polycyclic presentation:
2,7,2,29^2|a^2=c,d^a=d^17,e^a=e^28,e^b=e^16,d^c=d^28109 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 51);