Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1970 |
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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:
(1,2,3)(12,14,15,13,17,18,16,19);(2,3)(4,6,7,5)(9,11)(12,13,16,14,17,19,15,18);(2,3)(4,5,7,6)(8,9,10,11)(13,18)(14,19)(15,16)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,c^2=eg,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10712241, #10712246, #10712248, … |
| maximal normal subgroup of | #10712241, #10712246, #10712248, … |
| maximal quotient of | #10694051, #10694085, #10694349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4614);