Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C109 · Schur multiplier (H2) = C1 |
| direct product | C109×#1043⋊C3 |
| unambiguous semidirect product | #1043⋊(C3×C109) |
| Fitting, socle, Hall | C52×C109 ⋊ C3×C4 |
| derived, Sylow | C52 ⋊ C3×C4×C109 |
| Hall | #1043×C109 ⋊ C3 |
| Hall | C52⋊C3×C109 ⋊ C4 |
| Hall | #1043 ⋊ C3×C109 |
| Hall | C52⋊C3 ⋊ C4×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | #1043⋊C3 |
| commutator, hypocenter | C52 | C3×C4×C109 |
| Frattini | C1 | G |
| Fitting, socle | C52×C109 | C3×C4 |
| prime radical | C109×(C5⋊D5)⋊C3 | C2 |
| cosocle | C5⋊D5 | C2×C3×C109 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C109 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1635 |
1526 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 93);