Finite Group DatabasebetaFinite Group Databasebeta| order | 408 |
| isoclinism | isoclinic class of C3⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊#595 |
| unambiguous semidirect product | (C2×C3)⋊#595 |
| unambiguous semidirect product | D17⋊Dic3 |
| Fitting, socle | C2×C3×C17 ⋊ C4 |
| derived, Hall | C3×C17 ⋊ C2×C4 |
| Sylow | C17 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C2×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊#595 |
| commutator, hypocenter | C3×C17 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C17 | C4 |
| prime radical | C2×C3×D17 | C2 |
| cosocle | C3×D17 | C22 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 102 |
A minimal faithful permutation representation — 2 generators on 22 points:
(4,5)(7,8,9,11)(10,13,14,19)(12,15,17,16)(18,20,21,22);(1,2)(3,4,5)(6,7,10,15,8,12,18,20,13,19,22,21,17,11,16,14,9)36 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#595, (C2×D3)⋊#595, Dic3⋊#595, … |
| maximal normal subgroup of | Dic3×#595, (C2×D3)⋊#595, Dic3⋊#595, … |
| maximal quotient of | #11717844, #11717845, C4×C3⋊#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(408, 40);