Finite Group DatabasebetaFinite Group Databasebeta| order | 324 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×H(3,𝔽3) ⋊ C3 |
| Sylow | C22 ⋊ AΣL(1,𝔽27) |
51 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 36 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,4)(2,3)(5,6,9)(7,10,13)(8,12,11);(2,3,4)(6,8,10)Polycyclic presentation:
3^4,2^2|b^a=bc,e^a=f,f^a=ef,c^b=cd28 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(324, 55);