Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | Aut(G) = C2×D3×AGL(1,𝔽13) (order 1872) · Inn(G) = C3⋊#261 · Out(G) = C22×C3 |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#261 |
| unambiguous semidirect product | C3⋊(C3×#261) |
| Fitting, socle, Hall | C32×C13 ⋊ C4 |
| derived | C3×C13 ⋊ C3×C4 |
| Sylow | C13 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ #261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13 | C4 |
| prime radical | C32×D13 | C2 |
| cosocle | C3×D13 | C2×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C3 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 78 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(5,6)(8,12,10,9)(11,16,15,14)(13,17,19,18);(4,5,6)(7,8,11,16,18,9,13,19,12,17,14,15,10)45 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#261, D3×C3⋊#261, (C3⋊#261)⋊D3, … |
| maximal normal subgroup of | C3×D3×#261, D3×C3⋊#261, (C3⋊#261)⋊D3, … |
| maximal quotient of | C3×C3⋊#1057, C2×C3×C3⋊#261, C3×C9⋊#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 37);