Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C3×#486 ⋊ C2 |
| Sylow | C3 ⋊ #1697 |
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(5,9)(7,11)(8,10)(13,17)(16,19);(1,2,3)(5,8)(9,10)(12,13,14,16,15,17,18,19);(4,5)(6,8)(7,9)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=dg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,e^c=eg,h^c=h^245 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1697, C2×#71202, #10777764, … |
| maximal normal subgroup of | D3×#1697, C2×#71202, #10777764, … |
| maximal quotient of | #10688288, #10691385, #10691427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3778);