Finite Group DatabasebetaFinite Group Databasebeta| order | 9300 |
| isoclinism | isoclinic class of D31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C25×D31⋊C3 |
| unambiguous semidirect product | (C2×C25×D31)⋊C3 |
| Fitting | C2×C25×C31 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C22×C3×C25 |
| Hall | C2×C25×D31 ⋊ C3 |
| Hall | C25×C31⋊C3 ⋊ C22 |
| Hall | C25×C31 ⋊ C22×C3 |
| Hall | C2×D31 ⋊ C3×C25 |
| Hall | C31⋊C3 ⋊ C22×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D31⋊C3 |
| commutator, hypocenter | C31 | C22×C3×C25 |
| Frattini | C5 | C2×C5×D31⋊C3 |
| Fitting | C2×C25×C31 | C2×C3 |
| socle | C2×C5×C31 | C2×C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C25 | |
60 conjugacy classes of subgroups.
550 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C25×D31⋊C3, C2×C3×C25×D31⋊C3, C2×C25×C3⋊(D31⋊C3) |
| maximal normal subgroup of | C2×C3×C25×D31⋊C3 |
| maximal quotient of | C2×C25×D31⋊C9, D3×C25×D31⋊C3, C2×C3×C25×D31⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9300, 31);