Finite Group DatabasebetaFinite Group Databasebeta| order | 25092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D697⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C17×C41 ⋊ C22 |
| Hall | C17×C41 ⋊ C2×C3⋊D3 |
| Hall | C32×C41 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C2×D41 |
| Sylow | C41 ⋊ C3⋊D3×D17 |
| Sylow | C17 ⋊ C3⋊D3×D41 |
| Sylow | C32 ⋊ D17×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C17×C41 | C22 |
| LCS | G ▷ C32×C17×C41 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6273 |
Polycyclic presentation:
2^2,3^2,17,41|e^a=e^16,f^a=f^40,c^b=c^2,d^b=d^2,e^b=e^161620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25092, 100);