Finite Group DatabasebetaFinite Group Databasebeta| order | 2116 |
| isoclinism | isoclinic class of D232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D232 |
| unambiguous semidirect product | (C23×D23)⋊C2 |
| unambiguous semidirect product | (C23⋊D23)⋊C2 |
| Fitting, socle, derived, Sylow | C232 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C232 | C22 |
| LCS | G ▷ C232 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 46 |
169 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D232, D23×D161, D161⋊D23, … |
| maximal normal subgroup of | C7×D232, D23×AGL(1,𝔽23), #26042787⋊C2, … |
| maximal quotient of | C7×D232, D23×D161, D161⋊D23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2116, 9);