Finite Group DatabasebetaFinite Group Databasebeta| order | 18798 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D241⋊C3 |
| unambiguous semidirect product | D241⋊(C3×C13) |
| unambiguous semidirect product | (C241⋊C3)⋊(C2×C13) |
| Fitting, socle, Hall | C13×C241 ⋊ C2×C3 |
| derived, Sylow | C241 ⋊ C2×C3×C13 |
| Hall | C13×C241⋊C3 ⋊ C2 |
| Hall | C13×D241 ⋊ C3 |
| Hall | C241⋊C3 ⋊ C2×C13 |
| Hall | D241 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D241⋊C3 |
| commutator, cosocle, hypocenter | C241 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C241 | C2×C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3133 |
598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#11757210⋊C3, #49178119, D13×D241⋊C3, … |
| maximal normal subgroup of | C13×#11757210⋊C3, #49178119, D13×D241⋊C3, … |
| maximal quotient of | C13×Dic241⋊C3, C2×C13×D241⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18798, 13);