Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×#335 ⋊ C2 |
| Sylow | C3 ⋊ #1686 |
168 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 55 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:
(1,2)(5,9)(8,11)(12,13,15,17)(14,19,18,16);(4,5,6,8,7,9,10,11);(2,3)(5,8)(6,10)(9,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=d,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^2,c^b=cf,e^c=eg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1686, C2×#68592, #10777795, … |
| maximal normal subgroup of | D3×#1686, C2×#68592, #10777795, … |
| maximal quotient of | #10688277, #10691416, #10691430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1168);