Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | #1044×C109⋊C3 |
| unambiguous semidirect product | (#1044×C109)⋊C3 |
| Fitting, socle, derived, Hall | C52×C109 ⋊ C3×C4 |
| Hall | #1044×C109 ⋊ C3 |
| Hall | C52×C109⋊C3 ⋊ C4 |
| Sylow | C109 ⋊ C3×#1044 |
| Sylow | C52 ⋊ C4×C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C109 | C3×C4 |
| prime radical | C5⋊D5×C109⋊C3 | C2 |
| cosocle | C5⋊D5×C109 | C2×C3 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1090 |
390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 126);