Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C31⋊#3874 |
| unambiguous semidirect product | (C2×C31)⋊#3874 |
| Fitting, socle | C2×C52×C31 ⋊ D3 |
| derived, Hall | C31×C52⋊C3 ⋊ C22 |
| Hall | C52×C31 ⋊ C2×D3 |
| Hall | C52⋊C3 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×#3874 |
| Sylow | C52 ⋊ C2×D93 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C31⋊#3874 |
| commutator, hypocenter | C31×C52⋊C3 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C31 | D3 |
| LCS | G ▷ C31×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
356 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C31⋊C3)⋊#3874, D3×C31⋊#3874, C2×C3×C31⋊#3874, … |
| maximal normal subgroup of | C2×(C31⋊C3)⋊#3874, C2×C3×C31⋊#3874 |
| maximal quotient of | C2×C31⋊#90646, D3×C31⋊#3874, C2×C3×C31⋊#3874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 155);