Finite Group DatabasebetaFinite Group Databasebeta| order | 32705 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C211 ⋊ C5 |
| Sylow | C211 ⋊ ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C211⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C211 | C5 |
| LCS | G ▷ C31×C211 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6541 |
Polycyclic presentation:
5,31,211|b^a=b^4,c^a=c^551313 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32705, 4);