Finite Group DatabasebetaFinite Group Databasebeta| order | 2116 |
| isoclinism | isoclinic class of C23⋊D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C23⋊Dic23 |
| derived, Sylow | C232 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C23⋊D23 |
| commutator, hypocenter | C232 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C232 | C2 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C2 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2116 |
Polycyclic presentation:
2,23^2,2|a^2=d,b^a=b^22,c^a=c^22532 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C23⋊Dic23, C7⋊(C23⋊Dic23), C23⋊(C23⋊#157), … |
| maximal normal subgroup of | C7×C23⋊Dic23, #37551726, #37551727, … |
| maximal quotient of | C7×C23⋊Dic23, C7⋊(C23⋊Dic23), C23⋊(C23⋊#157), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2116, 7);