Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, hypercenter | C2 | PΓL(2,𝔽9) |
| commutator, socle, cosocle | C2×A6 | C22 |
| prime radical | C2×S6 | C2 |
| hypocenter | A6 | D4 |
| LCS | G ▷ C2×A6 ▷ A6 | |
| UCS | C1 ◁ C2 | |
167 conjugacy classes of subgroups; only the 8 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 8 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,2)(3,4)(5,6)(7,11,8,12,13,10,14,9);(1,4,3,2)(5,11,13,10,9,14,8,7)23 conjugacy classes — view the full character table.
| maximal quotient of | #72224456 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(3,4)(5,6)(7,11,8,12,13,10,14,9), (1,4,3,2)(5,11,13,10,9,14,8,7));