Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×D109⋊(C52⋊C3) |
| unambiguous semidirect product | D109⋊(C2×C52⋊C3) |
| unambiguous semidirect product | (C2×D109)⋊(C52⋊C3) |
| Fitting, socle | C2×C52×C109 ⋊ C2×C3 |
| derived, Hall | C52×C109 ⋊ C22×C3 |
| Hall | C2×C52×D109 ⋊ C3 |
| Hall | C52⋊(C109⋊C3) ⋊ C22 |
| Hall | C2×D109 ⋊ C52⋊C3 |
| Sylow | C109 ⋊ C22×C52⋊C3 |
| Sylow | C52 ⋊ C2×D109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D109⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C109 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C109 | C2×C3 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3270 |
944 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 127);