Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#555 ⋊ C2 |
| Sylow | C3 ⋊ #2204 |
236 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 45 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:
(1,3)(4,11)(5,6)(7,8)(9,13)(12,14)(17,18,19);(2,7)(3,5)(4,12)(8,10)(9,15)(13,16);(1,2)(3,9)(4,7)(5,13)(6,10)(8,12)(11,16)(14,15)(18,19)Polycyclic presentation:
2^7,3|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^2,c^b=cg,d^b=dg,e^b=efg,d^c=df,e^c=eg,e^d=eg45 conjugacy classes — view the full character table.
| maximal subgroup of | #10715944, #10715945, #10715949, … |
| maximal normal subgroup of | #10715944, #10715945, #10715949, … |
| maximal quotient of | #10707268, #10707274, #10707438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4506);