Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C31⋊#1043 |
| Fitting, socle, Hall | C3×C52×C31 ⋊ C4 |
| derived, Hall | C52×C31 ⋊ C3×C4 |
| Hall | C3×C31 ⋊ #1043 |
| Hall | C3×C52 ⋊ Dic31 |
| Sylow | C31 ⋊ C3×#1043 |
| Sylow | C52 ⋊ C3×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C31⋊#1043 |
| commutator, hypocenter | C52×C31 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C4 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
660 conjugacy classes — view the full character table.
| maximal subgroup of | (C31⋊C9)⋊#1043, #42124508, #42124510, … |
| maximal normal subgroup of | (C31⋊C9)⋊#1043, #42124508, #42124510, … |
| maximal quotient of | C9×C31⋊#1043, C32×C31⋊#1043, C3×C3⋊(C31⋊#1043) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 167);