Finite Group DatabasebetaFinite Group Databasebeta| order | 2418 |
| isoclinism | isoclinic class of #11925881 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#11925881 |
| Fitting, socle, Hall | C2×C13×C31 ⋊ C3 |
| derived, Hall | C13×C31 ⋊ C2×C3 |
| Hall | C2×C31 ⋊ C13⋊C3 |
| Sylow | C31 ⋊ C2×C13⋊C3 |
| Hall | C2×C13 ⋊ C31⋊C3 |
| Sylow | C13 ⋊ C2×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11925881 |
| commutator, cosocle, hypocenter | C13×C31 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C31 | C3 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 806 |
274 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#11925881, #18012812, #18012816, … |
| maximal normal subgroup of | C4×#11925881, #18012812, #18012816, … |
| maximal quotient of | C4×#11925881, C22×#11925881, C2×C5×#11925881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2418, 5);