Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#339 ⋊ C2 |
| Sylow | C3 ⋊ #1906 |
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(4,6)(5,10)(7,15)(8,13)(9,17)(11,18)(12,19)(14,16);(2,3)(4,6)(5,9,11,19)(7,15)(8,13)(10,17,18,12)(14,16);(4,5)(6,9,13,19)(7,12)(8,11)(10,14,18,15)(16,17)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,e^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,e^b=eg,f^b=fg,h^b=h^2,d^c=dg,e^c=eg,f^c=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1906, C2×#68778, #10797098, … |
| maximal normal subgroup of | D3×#1906, C2×#68778, #10797098, … |
| maximal quotient of | #10690653, #10690660, #10690667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1354);