Finite Group DatabasebetaFinite Group Databasebeta| order | 25767 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C409 ⋊ C9 |
| Sylow | C409 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ C409⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #22575221 |
| commutator, hypocenter | C7×C409 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C409 | C3 |
| LCS | G ▷ C7×C409 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25767 |
Polycyclic presentation:
3,7,409,3|a^3=d,b^a=b^2,c^a=c^532871 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25767, 4);