Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of C3⋊(D13⋊C3) |
| automorphism | Aut(G) = C2×D3×AGL(1,𝔽13) (order 1872) · Inn(G) = C3⋊(D13⋊C3) · Out(G) = C2×C4 |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(D13⋊C3) |
| unambiguous semidirect product | (C2×C3)⋊(D13⋊C3) |
| unambiguous semidirect product | (C2×C13⋊C3)⋊D3 |
| unambiguous semidirect product | (C2×D39)⋊C3 |
| Fitting, socle | C2×C3×C13 ⋊ C2×C3 |
| derived | C3×C13 ⋊ C22×C3 |
| Hall | C3×C13⋊C3 ⋊ C22 |
| Sylow | C13 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(D13⋊C3) |
| commutator, cosocle, hypocenter | C3×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13 | C2×C3 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 78 |
A minimal faithful permutation representation — 2 generators on 18 points:
(4,5)(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)30 conjugacy classes — view the full character table.
| maximal subgroup of | #64601⋊C3, #64603⋊C3, #64604⋊C3, … |
| maximal normal subgroup of | #64601⋊C3, #64603⋊C3, #64604⋊C3, … |
| maximal quotient of | Dic78⋊C3, C4×C3⋊(D13⋊C3), C4⋊(C3⋊(D13⋊C3)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 35);