Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C31 · Schur multiplier (H2) = C5 |
| direct product | C3×C31×#1044 |
| Fitting, socle, Hall | C3×C52×C31 ⋊ C4 |
| derived, Sylow | C52 ⋊ C3×C4×C31 |
| Hall | C52×C31 ⋊ C3×C4 |
| Hall | C3×C52 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | #1044 |
| commutator, hypocenter | C52 | C3×C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C4 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C31 | |
64 conjugacy classes of subgroups.
930 conjugacy classes — view the full character table.
| maximal subgroup of | #1044×C31⋊C9, C9×C31×#1044, C3×C31×#64480, … |
| maximal normal subgroup of | #1044×C31⋊C9, C9×C31×#1044, C3×C31⋊C3×#1044, … |
| maximal quotient of | C9×C31×#1044, C32×C31×#1044, C3×C31×C3⋊#1044 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 168);