Finite Group DatabasebetaFinite Group Databasebeta| order | 4324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D47 |
| unambiguous semidirect product | (D23×C47)⋊C2 |
| unambiguous semidirect product | (C23×D47)⋊C2 |
| unambiguous semidirect product | D1081⋊C2 |
| Fitting, socle, derived, Hall | C23×C47 ⋊ C22 |
| Sylow | C47 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C47 | C22 |
| LCS | G ▷ C23×C47 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 70 |
| transitive degree | μt(G) = 1081 |
325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D23×D47, D47×D69, D23×D141, … |
| maximal normal subgroup of | C3×D23×D47, C5×D23×D47, C7×D23×D47 |
| maximal quotient of | C3×D23×D47, D47×D69, D23×D141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4324, 10);