Finite Group DatabasebetaFinite Group Databasebeta| order | 4554 |
| isoclinism | isoclinic class of AGL(1,𝔽23) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C32×C23 ⋊ C2×C11 |
| derived, Sylow | C23 ⋊ C2×C32×C11 |
| Hall | C32×C23⋊C11 ⋊ C2 |
| Hall | C32×D23 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×C32 |
| Hall | D23 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C23 | C2×C32×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C23 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 207 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3)(8,11,12,19,20,27,22,23,13,24,25,9,10,14,15,26,21,16,28,17,18,29);(4,5,6)(7,8,10,13,12,16,18,26,15,21,23,29,25,28,27,19,20,24,22,14,17,11,9)207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4554, 14);