Finite Group DatabasebetaFinite Group Databasebeta| order | 23850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C5 |
| direct product | C53×C3⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | C3⋊(C53×(C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C3⋊(C5⋊D5))⋊(C3×C53) |
| unambiguous semidirect product | (C53×C3⋊(C5⋊D5))⋊C3 |
| Fitting, socle | C3×C52×C53 ⋊ C2×C3 |
| derived | C3×C52 ⋊ C2×C3×C53 |
| Hall | C3×C53×C52⋊C3 ⋊ C2 |
| Hall | C52×C53 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×C53 |
| Sylow | C52 ⋊ C3×D3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C3⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C3×C52 | C2×C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C53 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C53 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2385 |
1113 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23850, 49);