Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C41 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×C41×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C5×C41 | A5 |
| commutator, hypocenter | A5 | C3×C5×C41 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C3×C5×C41 | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 3075 |
A minimal faithful permutation representation — 2 generators on 54 points:
(9,10,13,11,12);(1,2,3)(4,5,6,7,8)(9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54)3075 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 622);