Finite Group DatabasebetaFinite Group Databasebeta| order | 2162 |
| isoclinism | isoclinic class of C47⋊C23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C2×C47⋊C23 |
| unambiguous semidirect product | (C2×C47)⋊C23 |
| Fitting, socle, Hall | C2×C47 ⋊ C23 |
| derived, Sylow | C47 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C47⋊C23 |
| commutator, cosocle, hypocenter | C47 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C47 | C23 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 94 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | Dic47⋊C23, C4×C47⋊C23, C2×AGL(1,𝔽47), … |
| maximal normal subgroup of | Dic47⋊C23, C4×C47⋊C23, C2×AGL(1,𝔽47), … |
| maximal quotient of | C4×C47⋊C23, C22×C47⋊C23, C2×C5×C47⋊C23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2162, 2);