Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×#1043 |
| Fitting, socle, derived, Hall | C52×C31 ⋊ C3×C4 |
| Hall | C31×#1043 ⋊ C3 |
| Hall | C52×C31⋊C3 ⋊ C4 |
| Sylow | C31 ⋊ C3×#1043 |
| Sylow | C52 ⋊ C4×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C31 | C3×C4 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
130 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#1043⋊C3, C3×C31⋊C3×#1043, C31⋊C3×C3⋊#1043 |
| maximal normal subgroup of | C31⋊C3×#1043⋊C3, C3×C31⋊C3×#1043 |
| maximal quotient of | #1043×C31⋊C9, C3×C31⋊C3×#1043, C31⋊C3×C3⋊#1043 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 121);