Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #1519 |
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(6,11)(8,10)(12,14,16,15)(13,17,19,18);(2,3)(4,6)(5,8)(7,11)(9,10)(13,17)(14,15)(18,19);(2,3)(4,5)(6,10,11,8)(7,9)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^2,c^b=cf,d^b=dg,e^b=efg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10686716, #10686717, #10686727, … |
| maximal normal subgroup of | #10686716, #10686717, #10686727, … |
| maximal quotient of | #10683171, #10683175, #10683237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2520);