Finite Group DatabasebetaFinite Group Databasebeta| order | 18676 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊AGL(1,𝔽29) |
| unambiguous semidirect product | (C23⋊#1181)⋊C7 |
| Fitting, socle, derived, Hall | C23×C29 ⋊ C4×C7 |
| Hall | C23×C29⋊C7 ⋊ C4 |
| Hall | C23⋊#1181 ⋊ C7 |
| Hall | C29⋊C7 ⋊ Dic23 |
| Sylow | C29 ⋊ C7×Dic23 |
| Sylow | C23 ⋊ AGL(1,𝔽29) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C29 | C4×C7 |
| prime radical | C23×D29⋊C7 | C2 |
| cosocle | C23×D29 | C2×C7 |
| LCS | G ▷ C23×C29 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 667 |
Polycyclic presentation:
2,7,2,23,29|a^2=c,d^a=d^22,e^a=e^17,e^b=e^16,e^c=e^28205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18676, 15);