Finite Group DatabasebetaFinite Group Databasebeta| order | 4300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D25×D43 |
| unambiguous semidirect product | (C43×D25)⋊C2 |
| unambiguous semidirect product | (C25×D43)⋊C2 |
| unambiguous semidirect product | D1075⋊C2 |
| Fitting, derived, Hall | C25×C43 ⋊ C22 |
| Sylow | C43 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C43 | C22 |
| Frattini | C5 | D5×D43 |
| socle | C5×C43 | C2×D5 |
| LCS | G ▷ C25×C43 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 68 |
| transitive degree | μt(G) = 1075 |
322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D25×D43⋊C3, C3×D25×D43, D43×D75, … |
| maximal normal subgroup of | D25×D43⋊C3, C3×D25×D43, D25×D43⋊C7, … |
| maximal quotient of | C3×D25×D43, D43×D75, D25×D129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4300, 8);