Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C109 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C109×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C2×C5⋊D5)⋊(C3×C109) |
| Fitting, socle | C2×C52×C109 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C22×C3×C109 |
| Hall | C2×C5⋊D5×C109 ⋊ C3 |
| Hall | C52⋊C3×C109 ⋊ C22 |
| Hall | C52×C109 ⋊ C22×C3 |
| Hall | C2×C5⋊D5 ⋊ C3×C109 |
| Hall | C52⋊C3 ⋊ C22×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C109 | (C5⋊D5)⋊C3 |
| commutator, cosocle, hypocenter | C52 | C22×C3×C109 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C109 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C109 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3270 |
2180 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 131);