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 ⋊ #1935 |
248 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 91 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)(9,11)(12,14,15,13,17,18,16,19);(2,3)(4,6,7,5)(12,13,15,18,17,19,16,14);(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=df,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,c^b=cg,h^b=h^2,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1935, C2×#69675, #10797821, … |
| maximal normal subgroup of | D3×#1935, C2×#69675, #10797821, … |
| maximal quotient of | #10693461, #10693489, #10693559, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2251);