Finite Group DatabasebetaFinite Group Databasebeta| order | 11396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic259 |
| unambiguous semidirect product | C7⋊(C11×Dic37) |
| derived, Hall | C7×C37 ⋊ C4×C11 |
| Hall | C7×C11×C37 ⋊ C4 |
| Hall | C11×C37 ⋊ Dic7 |
| Hall | C7×C11 ⋊ Dic37 |
| Sylow | C37 ⋊ C11×Dic7 |
| Sylow | C7 ⋊ C11×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D259 |
| commutator, hypocenter | C7×C37 | C4×C11 |
| Frattini | C2 | C11×D259 |
| Fitting, socle, prime radical | C2×C7×C11×C37 | C2 |
| cosocle | C2×C7×C37 | C2×C11 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
2882 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic259, C11×Dic777, C11×#15690918, … |
| maximal normal subgroup of | C3×C11×Dic259, C11×#15690918, C11×ΓL(1,𝔽8)⋊Dic37, … |
| maximal quotient of | C3×C11×Dic259, C11×Dic777 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11396, 6);