Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16809850⋊C7 |
| Fitting, derived, Sylow | C841 ⋊ C4×C7 |
| Hall | C841⋊C7 ⋊ C4 |
| Hall | #16809850 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C841 | C4×C7 |
| Frattini, socle | C29 | AGL(1,𝔽29) |
| prime radical | D841⋊C7 | C2 |
| cosocle | D841 | C2×C7 |
| LCS | G ▷ C841 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 841 |
Polycyclic presentation:
2,7,2,29^2|a^2=c,d^29=e^14,d^a=d^17e,e^a=e^17,d^b=d^16e^26,e^b=e^16,d^c=d^28e^15,e^c=e^2858 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 8);