Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1884 |
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 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)(4,7)(5,11)(6,15)(8,14)(9,10)(12,17)(13,16)(18,19);(2,3)(4,6,8,11,9,17,19,16)(5,10,12,18,13,7,15,14);(2,3)(4,5)(6,14,17,18)(7,11,10,16)(8,12)(9,13)(15,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,d^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,d^b=dg,e^b=eg,f^b=fg,h^b=h^2,d^c=dg,f^c=fg60 conjugacy classes — view the full character table.
| maximal subgroup of | #10682916, #10682918, #10682922, … |
| maximal normal subgroup of | #10682916, #10682918, #10682922, … |
| maximal quotient of | #10689833, #10689838, #10689843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4393);