Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1911 |
362 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 93 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(5,11)(7,8)(10,18)(14,16);(2,3)(4,6)(5,10,11,18)(7,14)(8,16)(9,15)(12,13,17,19);(2,3)(4,5,8,12,9,11,7,17)(6,13,16,18,15,19,14,10)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,h^b=h^2,d^c=dg,f^c=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | #10710945, #10710946, #10710952, … |
| maximal normal subgroup of | #10710945, #10710946, #10710952, … |
| maximal quotient of | #10690683, #10690693, #10690703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4429);