Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of #11761914 |
| automorphism | Aut(G) = PΓL(2,𝔽9) (order 1440) · Inn(G) = A6 · Out(G) = C22 |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, cosocle, hypercenter | C3 | A6 |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 ◁ C3 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,3,6)(2,5,9)(4,8,12)(7,14,13)(10,11,17)(15,16,18);(1,2,4)(3,7,14)(5,10,11)(6,12,9)(8,15,16)17 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 260);