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 ⋊ #1847 |
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 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) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(8,9,10,11)(13,17)(16,19);(2,3)(12,13,14,16,15,17,18,19);(2,3)(4,5,6,7)(9,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,c^2=e,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,c^b=cg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10682605, #10682607, #10689542, … |
| maximal normal subgroup of | #10682605, #10682607, #10689542, … |
| maximal quotient of | #10688937, #10688952, #10688971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2126);