Finite Group DatabasebetaFinite Group Databasebeta| order | 16247 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C211⋊C7 |
| unambiguous semidirect product | C211⋊(C7×C11) |
| unambiguous semidirect product | (C11×C211)⋊C7 |
| Fitting, socle, Hall | C11×C211 ⋊ C7 |
| derived, Sylow | C211 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C211⋊C7 |
| commutator, cosocle, hypocenter | C211 | C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C211 | C7 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2321 |
407 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×C211⋊C7, C11×D211⋊C7, D11×C211⋊C7, … |
| maximal normal subgroup of | C2×C11×C211⋊C7, C11×D211⋊C7, D11×C211⋊C7, … |
| maximal quotient of | C2×C11×C211⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16247, 1);