Finite Group DatabasebetaFinite Group Databasebeta| order | 11684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D127 |
| unambiguous semidirect product | (D23×C127)⋊C2 |
| unambiguous semidirect product | (C23×D127)⋊C2 |
| unambiguous semidirect product | D2921⋊C2 |
| Fitting, socle, derived, Hall | C23×C127 ⋊ C22 |
| Sylow | C127 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C127 | C22 |
| LCS | G ▷ C23×C127 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
845 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D127⋊C3, C3×D23×D127, D69×D127, … |
| maximal normal subgroup of | D23×D127⋊C3, C3×D23×D127 |
| maximal quotient of | C3×D23×D127, D69×D127, D23×D381, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11684, 6);