Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×AGL(1,𝔽5)×C31⋊C3 |
| unambiguous semidirect product | (C5×AGL(1,𝔽5)×C31)⋊C3 |
| Fitting, socle, Hall | C52×C31 ⋊ C3×C4 |
| derived | C5×C31 ⋊ C3×C4×C5 |
| Hall | C5×AGL(1,𝔽5)×C31 ⋊ C3 |
| Hall | C52×C31⋊C3 ⋊ C4 |
| Sylow | C31 ⋊ C3×C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ C4×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | AGL(1,𝔽5)×C31⋊C3 |
| commutator, hypocenter | C5×C31 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C31 | C3×C4 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
325 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×AGL(1,𝔽5)×C31⋊C3, C5×ΓL(1,𝔽16)×C31⋊C3 |
| maximal normal subgroup of | C3×C5×AGL(1,𝔽5)×C31⋊C3 |
| maximal quotient of | C5×AGL(1,𝔽5)×C31⋊C9, C3×C5×AGL(1,𝔽5)×C31⋊C3, C5×ΓL(1,𝔽16)×C31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 118);