Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #3874⋊D109 |
| Fitting, socle, Hall | C52×C109 ⋊ C2×D3 |
| derived, Hall | C52⋊C3×C109 ⋊ C22 |
| Sylow | C109 ⋊ #3874⋊C2 |
| Hall | C52⋊C3 ⋊ C2×D109 |
| Sylow | C52 ⋊ D3×D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52⋊C3×C109 | C22 |
| Fitting, socle | C52×C109 | C2×D3 |
| LCS | G ▷ C52⋊C3×C109 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1635 |
Polycyclic presentation:
2^2,3,109,5^2|c^a=c^2,d^a=d^108,e^a=ef,f^a=f^4,c^b=c^2,e^b=e^4f^4,e^c=f,f^c=e^4f^4716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 102);