Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C5×C7 |
| direct product | C72×C3⋊(C5⋊D5) |
| unambiguous semidirect product | C3⋊(C72×C5⋊D5) |
| unambiguous semidirect product | C5⋊(C72×D15) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C2 |
| derived, Hall | C3×C52 ⋊ C2×C72 |
| Hall | C52×C72 ⋊ D3 |
| Hall | C3×C72 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D3×C72 |
| Sylow | C3 ⋊ C72×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C3⋊(C5⋊D5) |
| commutator, hypocenter | C3×C52 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C72 | |
320 conjugacy classes of subgroups.
1911 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 153);