Finite Group DatabasebetaFinite Group Databasebeta| order | 4300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C43 · Schur multiplier (H2) = C2 |
| direct product | D52×C43 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C43) |
| unambiguous semidirect product | (C5⋊D5)⋊(C2×C43) |
| Fitting, socle, Hall | C52×C43 ⋊ C22 |
| derived, Sylow | C52 ⋊ C22×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D52 |
| commutator, cosocle, hypocenter | C52 | C22×C43 |
| Frattini | C1 | G |
| Fitting, socle | C52×C43 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C43 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 430 |
688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D52×C43⋊C3, C43×#3874⋊C2, C3×D52×C43, … |
| maximal normal subgroup of | D52×C43⋊C3, C3×D52×C43, D52×C43⋊C7, … |
| maximal quotient of | C3×D52×C43, D5×D15×C43, C43×D15⋊D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4300, 29);