Finite Group DatabasebetaFinite Group Databasebeta| order | 1012 |
| isoclinism | isoclinic class of AGL(1,𝔽23) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic23⋊C11 |
| unambiguous semidirect product | (C23⋊C11)⋊C4 |
| derived, Sylow | C23 ⋊ C4×C11 |
| Hall | C23⋊C11 ⋊ C4 |
| Hall | Dic23 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽23) |
| commutator, hypocenter | C23 | C4×C11 |
| Fitting, socle, cosocle | C2×C23 | C2×C11 |
| prime radical | C2×C23⋊C11 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 92 |
Polycyclic presentation:
2,11,2,23|a^2=c,d^a=d^22,d^b=d^446 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic23⋊C11, C3⋊(Dic23⋊C11), C11×Dic23⋊C11, … |
| maximal normal subgroup of | C3×Dic23⋊C11, C11×Dic23⋊C11, C13×Dic23⋊C11, … |
| maximal quotient of | C3×Dic23⋊C11, C3⋊(Dic23⋊C11), Dic23⋊C121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1012, 1);