Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | Aut(G) = C2×C3×AGL(1,𝔽13) (order 936) · Inn(G) = D13⋊C3 · Out(G) = C22×C3 |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D13⋊C9 |
| unambiguous semidirect product | D13⋊(C2×C9) |
| unambiguous semidirect product | (C2×D13)⋊C9 |
| unambiguous semidirect product | (C13⋊C9)⋊C22 |
| unambiguous semidirect product | (C2×C13⋊C9)⋊C2 |
| derived, Sylow | C13 ⋊ C22×C9 |
| Hall | C13⋊C9 ⋊ C22 |
| Hall | C2×D13 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D13⋊C3 |
| commutator, hypocenter | C13 | C22×C9 |
| Frattini | C3 | C2×D13⋊C3 |
| Fitting, socle | C2×C3×C13 | C2×C3 |
| prime radical | C2×C3×D13 | C3 |
| cosocle | C3×C13 | C22×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 234 |
A minimal faithful permutation representation — 2 generators on 24 points:
(3,7,11,5,10,6,8,4,9)(13,17,18,14,15,19)(16,23,22,20,21,24);(1,2)(12,13,16,15,19,22,21,23,24,18,17,20,14)48 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D13⋊C9, C4⋊(D13⋊C9), (C22⋊D13)⋊C9, … |
| maximal normal subgroup of | C4×D13⋊C9, C4⋊(D13⋊C9), (C22⋊D13)⋊C9, … |
| maximal quotient of | Dic26⋊C9, C4×D13⋊C9, C4⋊(D13⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 8);