Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C31⋊C25 |
| unambiguous semidirect product | C3⋊(C22×C31⋊C25) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C31⋊C25) |
| unambiguous semidirect product | (C2×D3×C31)⋊C25 |
| derived, Hall | C3×C31 ⋊ C22×C25 |
| Hall | C3×C31⋊C25 ⋊ C22 |
| Hall | C2×D3×C31 ⋊ C25 |
| Sylow | C31 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C22×C31⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D3×ΓL(1,𝔽32) |
| commutator, hypocenter | C3×C31 | C22×C25 |
| Frattini | C5 | C2×D3×ΓL(1,𝔽32) |
| Fitting, socle | C2×C3×C5×C31 | C2×C5 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C2×C5 | |
60 conjugacy classes of subgroups.
330 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×C31⋊C25, C2×D3×(C31⋊C3)⋊C25, D32×C31⋊C25, … |
| maximal normal subgroup of | C2×D3×(C31⋊C3)⋊C25, C2×C3×D3×C31⋊C25 |
| maximal quotient of | C2×D9×C31⋊C25, D32×C31⋊C25, C2×C3×D3×C31⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 29);