Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1944 |
240 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 109 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) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(12,13,18,19,15,17,14,16);(4,6,7,5)(9,11)(13,17)(16,19);(2,3)(4,5,7,6)(8,9)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,c^2=eg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,c^b=cg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10681992, #10681994, #10681995, … |
| maximal normal subgroup of | #10681992, #10681994, #10681995, … |
| maximal quotient of | #10693739, #10693759, #10693869, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2396);