Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C2×C52×#3861 |
| Fitting, socle, Hall | C2×C52×C72 ⋊ C3 |
| derived, Sylow | C72 ⋊ C2×C3×C52 |
| Hall | C52×C72 ⋊ C2×C3 |
| Hall | C2×C72 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | #3861 |
| commutator, hypocenter | C72 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C72 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C52 | |
320 conjugacy classes of subgroups.
950 conjugacy classes — view the full character table.
| maximal subgroup of | C52×#10596874, C52×#10596873, C5×#15668734, … |
| maximal normal subgroup of | C52×#10596874, C52×#10596873, C5×#15668734, … |
| maximal quotient of | C4×C52×#3861, C22×C52×#3861, C2×C52×#89204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 133);