Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C292 ⋊ C4×C7 |
| Hall | #19154636 ⋊ C4 |
| Hall | C29×Dic29 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #26044460 |
| commutator, hypocenter | C292 | C4×C7 |
| Fitting, socle, cosocle | C2×C292 | C2×C7 |
| prime radical | C2×#19154636 | C2 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 812 |
Polycyclic presentation:
2,7,29^2,2|a^2=e,c^a=c^28,c^b=c^16,d^b=d^7160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 27);