Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D25×#3861 |
| unambiguous semidirect product | C25⋊(C2×#3861) |
| Fitting, derived, Hall | C72×C25 ⋊ C2×C3 |
| Hall | C25×#3861 ⋊ C2 |
| Hall | C72×D25 ⋊ C3 |
| Sylow | C72 ⋊ C3×D25 |
| Sylow | C25 ⋊ C2×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C72×C25 | C2×C3 |
| Frattini | C5 | D5×#3861 |
| socle | C5×C72 | C3×D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
266 conjugacy classes — view the full character table.
| maximal subgroup of | #28413029, #28413031, #1035×#3861, … |
| maximal normal subgroup of | #28413029, #28413031, #1035×#3861, … |
| maximal quotient of | Dic25×#3861, C2×D25×#3861, D25×#89204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 58);