Finite Group DatabasebetaFinite Group Databasebeta| order | 18135 |
| isoclinism | isoclinic class of ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C13 · Schur multiplier (H2) = C3 |
| direct product | C32×C13×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C32×C31)⋊(C5×C13) |
| unambiguous semidirect product | (C32×C13×C31)⋊C5 |
| Fitting, socle, Hall | C32×C13×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C32×C5×C13 |
| Hall | C13×C31 ⋊ C32×C5 |
| Hall | C32×C31 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C13 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C32×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C32×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3627 |
1287 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C13×D31⋊C5, C32×C13⋊(D31⋊C5), C32×D13×ΓL(1,𝔽32), … |
| maximal normal subgroup of | C32×C13×D31⋊C5, C32×C13⋊(D31⋊C5), C32×D13×ΓL(1,𝔽32), … |
| maximal quotient of | C2×C32×C13×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18135, 18);