Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C5⋊#64423 |
| unambiguous semidirect product | C5⋊(C5×#64423) |
| Fitting, socle, Hall | C52×C72 ⋊ C2×C3 |
| derived | C5×C72 ⋊ C2×C3×C5 |
| Hall | C52×#3861 ⋊ C2 |
| Hall | C5×C7×D35 ⋊ C3 |
| Hall | #3861 ⋊ C5×D5 |
| Sylow | C72 ⋊ C3×C5×D5 |
| Sylow | C52 ⋊ #64423 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊#64423 |
| commutator, hypocenter | C5×C72 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | C2×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C5 | |
128 conjugacy classes of subgroups.
275 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#64423⋊D5, C5×#64424⋊D5, C5×D5×#64423, … |
| maximal normal subgroup of | C5×#64423⋊D5, C5×#64424⋊D5, C5×D5×#64423, … |
| maximal quotient of | C5×#15668736, C2×C5×C5⋊#64423, C5×C5⋊#11725076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 88);