Finite Group DatabasebetaFinite Group Databasebeta| order | 2116 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×D23 |
| unambiguous semidirect product | C23⋊(C22×C23) |
| unambiguous semidirect product | (C2×C23)⋊(C2×C23) |
| Fitting, socle | C2×C232 ⋊ C2 |
| derived | C23 ⋊ C22×C23 |
| Sylow | C232 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D23 |
| commutator, cosocle, hypocenter | C23 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C232 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C23 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 92 |
598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C23×D23, C2×C23×D161, C2×C7×C23×D23, … |
| maximal normal subgroup of | C2×C7×C23×D23, C2×C23×AGL(1,𝔽23), C2×D23×C23⋊C11, … |
| maximal quotient of | D7×C23×D23, C2×C23×D161, C2×C7×C23×D23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2116, 12);