Finite Group DatabasebetaFinite Group Databasebeta| order | 32100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C107⋊#64480 |
| Fitting, socle, Hall | C52×C107 ⋊ Dic3 |
| derived, Hall | C52⋊C3×C107 ⋊ C4 |
| Sylow | C107 ⋊ #64480 |
| Hall | C52⋊C3 ⋊ Dic107 |
| Sylow | C52 ⋊ Dic321 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52⋊C3×C107 | C4 |
| Fitting, socle | C52×C107 | Dic3 |
| prime radical, cosocle | C107×(C5⋊D5)⋊C3 | C2 |
| LCS | G ▷ C52⋊C3×C107 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1605 |
Polycyclic presentation:
2^2,3,107,5^2|a^2=b,c^a=c^2,d^a=d^106,e^a=ef^4,f^a=e^2f^4,e^b=e^4,f^b=f^4,e^c=e^3f^2,f^c=ef538 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32100, 51);