Finite Group DatabasebetaFinite Group Databasebeta| order | 32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D109⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | #30654822⋊C2 |
| unambiguous semidirect product | ((C5⋊D5)⋊(C109⋊C3))⋊C2 |
| unambiguous semidirect product | (D109⋊(C52⋊C3))⋊C2 |
| Fitting, socle, derived, Hall | C52×C109 ⋊ C22×C3 |
| Hall | C5⋊D5×D109 ⋊ C3 |
| Hall | C52⋊(C109⋊C3) ⋊ C22 |
| Sylow | C109 ⋊ C2×(C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C2×D109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C109 | C22×C3 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1635 |
Polycyclic presentation:
2^2,3,5^2,109|f^a=f^108,d^b=d^4,e^b=e^4,d^c=de^3,e^c=d^4e^3,f^c=f^63272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32700, 87);