Finite Group DatabasebetaFinite Group Databasebeta| order | 2116 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic23 |
| unambiguous semidirect product | C23⋊(C4×C23) |
| derived | C23 ⋊ C4×C23 |
| Sylow | C232 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D23 |
| commutator, hypocenter | C23 | C4×C23 |
| Frattini | C2 | C23×D23 |
| Fitting, socle, prime radical | C2×C232 | C2 |
| cosocle | C2×C23 | C2×C23 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C23 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 92 |
598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C23×Dic23, C23×Dic161, C23×C23⋊#157, … |
| maximal normal subgroup of | C7×C23×Dic23, C23×Dic23⋊C11, #37551732, … |
| maximal quotient of | C7×C23×Dic23, C23×Dic161, C23×C23⋊#157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2116, 6);