Finite Group DatabasebetaFinite Group Databasebeta| order | 32100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C107⋊#1042) |
| unambiguous semidirect product | C107⋊(C3⋊#1042) |
| Fitting, socle, derived, Hall | C3×C52×C107 ⋊ C4 |
| Hall | C52×C107 ⋊ Dic3 |
| Hall | C3×C107 ⋊ #1042 |
| Sylow | C107 ⋊ C3⋊#1042 |
| Hall | C3×C52 ⋊ Dic107 |
| Sylow | C52 ⋊ Dic321 |
| Sylow | C3 ⋊ C107⋊#1042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C107 | C4 |
| prime radical, cosocle | C3×C5×D5×C107 | C2 |
| LCS | G ▷ C3×C52×C107 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6420 |
Polycyclic presentation:
2^2,3,5^2,107|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^106,d^b=d^43213 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32100, 84);