Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×D17×C52⋊C3 |
| unambiguous semidirect product | C17⋊(C22×C52⋊C3) |
| unambiguous semidirect product | (C2×C17)⋊(C2×C52⋊C3) |
| unambiguous semidirect product | (C2×C52×D17)⋊C3 |
| Fitting, socle | C2×C52×C17 ⋊ C2×C3 |
| derived, Hall | C52×C17 ⋊ C22×C3 |
| Hall | C2×C52×D17 ⋊ C3 |
| Hall | C17×C52⋊C3 ⋊ C22 |
| Sylow | C52 ⋊ C2×C3×D17 |
| Sylow | C17 ⋊ C22×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D17×C52⋊C3 |
| commutator, hypocenter | C52×C17 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C17 | C2×C3 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
220 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D17×C52⋊C3, C2×C3×D17×C52⋊C3, C2×C52⋊C3×D51, … |
| maximal normal subgroup of | C2×C3×D17×C52⋊C3, C2×C7×D17×C52⋊C3 |
| maximal quotient of | C2×D17×C52⋊C9, D3×D17×C52⋊C3, C2×C3×D17×C52⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 75);