Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | #595×C52⋊C3 |
| unambiguous semidirect product | (C52×#595)⋊C3 |
| Fitting, socle, derived, Hall | C52×C17 ⋊ C3×C4 |
| Hall | C52×#595 ⋊ C3 |
| Hall | C17×C52⋊C3 ⋊ C4 |
| Sylow | C52 ⋊ C3×#595 |
| Sylow | C17 ⋊ C4×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C17 | C3×C4 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
88 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#595×C52⋊C3, C52⋊C3×C3⋊#595, C7×#595×C52⋊C3, … |
| maximal normal subgroup of | C3×#595×C52⋊C3, C7×#595×C52⋊C3 |
| maximal quotient of | #595×C52⋊C9, C3×#595×C52⋊C3, C52⋊C3×C3⋊#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 70);