Finite Group DatabasebetaFinite Group Databasebeta| order | 16430 |
| isoclinism | isoclinic class of ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C53 · Schur multiplier (H2) = C1 |
| direct product | C2×C53×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C2×C31)⋊(C5×C53) |
| unambiguous semidirect product | (C2×C31×C53)⋊C5 |
| Fitting, socle, Hall | C2×C31×C53 ⋊ C5 |
| derived, Sylow | C31 ⋊ C2×C5×C53 |
| Hall | C31×C53 ⋊ C2×C5 |
| Hall | C2×C31 ⋊ C5×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C2×C5×C53 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C53 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C53 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3286 |
1166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C53×ΓL(1,𝔽32), ΓL(1,𝔽32)×Dic53, C53×Dic31⋊C5, … |
| maximal normal subgroup of | C4×C53×ΓL(1,𝔽32), ΓL(1,𝔽32)×Dic53, C53×Dic31⋊C5, … |
| maximal quotient of | C4×C53×ΓL(1,𝔽32), C22×C53×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16430, 2);