Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic841⋊C7 |
| derived, Sylow | C841 ⋊ C4×C7 |
| Hall | C841⋊C7 ⋊ C4 |
| Hall | Dic841 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D841⋊C7 |
| commutator, hypocenter | C841 | C4×C7 |
| Frattini, socle | C2×C29 | D29⋊C7 |
| Fitting, cosocle | C2×C841 | C2×C7 |
| prime radical | C2×C841⋊C7 | C2 |
| LCS | G ▷ C841 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3364 |
Polycyclic presentation:
2,7,29,2,29|a^2=d,c^29=e^28,c^a=c^28e,e^a=e^28,c^b=c^16e^23,e^b=e^16148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 2);