Finite Group DatabasebetaFinite Group Databasebeta| order | 17754 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×D269 |
| unambiguous semidirect product | C269⋊(C2×C3×C11) |
| Fitting, socle, Hall | C3×C11×C269 ⋊ C2 |
| derived, Sylow | C269 ⋊ C2×C3×C11 |
| Hall | C11×C269 ⋊ C2×C3 |
| Hall | C3×C269 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | D269 |
| commutator, cosocle, hypocenter | C269 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C269 | C2 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C3×C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8877 |
4488 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×#11761640, C3×C11⋊#11761640, C3×D11×D269, … |
| maximal normal subgroup of | C3×C11×#11761640, C3×C11⋊#11761640, C3×D11×D269, … |
| maximal quotient of | C3×C11×Dic269, C2×C3×C11×D269 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17754, 2);