Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | Aut(G) = C2×D3×AGL(1,𝔽13) (order 1872) · Inn(G) = D13⋊C3 · Out(G) = C22×D3 |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle | C2×C3×C13 ⋊ C2×C3 |
| derived, Sylow | C13 ⋊ C22×C32 |
| Hall | C3×C13⋊C3 ⋊ C22 |
| Hall | C2×D13 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 78 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2)(7,11,12,8,9,13)(10,17,16,14,15,18);(1,2)(3,4,5)(6,7,10,9,13,16,15,17,18,12,11,14,8)48 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×D13⋊C3, #64602⋊C3, #64603⋊C3, … |
| maximal normal subgroup of | Dic3×D13⋊C3, #64602⋊C3, #64603⋊C3, … |
| maximal quotient of | C3×(C13⋊C3)⋊Q8, C3×C4×D13⋊C3, C3×C4⋊(D13⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 33);