Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#353 ⋊ C2 |
| Sylow | C3 ⋊ #2126 |
258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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:
(2,3)(4,6,8,14)(5,10,12,18)(7,13,15,19)(9,16,11,17);(1,2,3)(5,9)(7,15)(10,16)(11,12)(13,19)(17,18);(4,5)(6,10)(7,11,15,9)(8,12)(13,17,19,16)(14,18)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,d^2=g,b^a=bd,d^a=df,f^a=fg,d^b=dg,e^b=efg,h^c=h^2,e^d=eg39 conjugacy classes — view the full character table.
| maximal subgroup of | #10715404, #10715412, #10715496, … |
| maximal normal subgroup of | #10715404, #10715412, #10715496, … |
| maximal quotient of | #10704290, #10704344, #10704458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1727);