Finite Group DatabasebetaFinite Group Databasebeta| order | 33852 |
| automorphism | ? |
| homology | Abelianization (H1) = C31 · Schur multiplier (H2) = C2 |
| direct product | C31×PSL(2,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C31 | PSL(2,𝔽13) |
| commutator, hypocenter | PSL(2,𝔽13) | C31 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽13) | |
| UCS | C1 ◁ C31 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 434 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,5,8)(2,3,7)(4,6,10)(11,12,14);(1,2)(3,4)(5,9)(7,11)(10,13)(12,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45)279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33852, 441);