Finite Group DatabasebetaFinite Group Databasebeta| order | 3645 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C5×C9 · Schur multiplier (H2) = C36 |
| direct product | C32×C5×C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C34×C5 | C32 |
| commutator | C3 | C33×C5×C9 |
| Frattini, cosocle | C32 | C34×C5 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C34×C5 ◁ G | |
1484 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 3645 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3)(25,26,27,28,29);(4,5,6);(8,10,13)(11,15,14)(16,17,19,18,20,22,21,23,24);(7,8,11,9,10,14,12,13,15)1485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3645, 417);