Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽32)×C11⋊AGL(1,𝔽5) |
| Fitting, socle, derived | C5×C11×C31 ⋊ C4×C5 |
| Hall | C5×C11×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C5×ΓL(1,𝔽32) ⋊ Dic11 |
| Hall | C11×C31 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C31 ⋊ C5×C11⋊AGL(1,𝔽5) |
| Sylow | C11 ⋊ AGL(1,𝔽5)×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C31 | C4×C5 |
| prime radical | D5×C11×ΓL(1,𝔽32) | C2 |
| cosocle | D5×C11×C31 | C2×C5 |
| LCS | G ▷ C5×C11×C31 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1705 |
275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 181);