Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1882 |
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 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) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(8,10)(9,14)(11,19)(12,20)(13,21)(15,18)(16,22)(17,23);(2,3)(4,6,7,5)(8,10)(9,14)(11,20)(12,19)(13,21)(15,22)(16,18)(17,23);(4,5,7,6)(8,9,12,16,13,17,11,15)(10,18,20,14,21,22,19,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,d^b=dg,f^b=fg,h^b=h^2,e^c=eg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1882, C2×#70365, #10796691, … |
| maximal normal subgroup of | D3×#1882, C2×#70365, #10796691, … |
| maximal quotient of | #10689802, #10689816, #10689904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2941);