Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#568 ⋊ C2 |
| Sylow | C3 ⋊ #1903 |
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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:
(1,2,3)(4,7)(5,11)(6,13)(8,17)(9,16)(10,18)(12,19)(14,15);(4,6,9,5,10,14,8,12)(7,13,16,11,18,15,17,19);(2,3)(4,5)(6,9)(7,15,18,13)(8,14)(10,12)(11,17,19,16)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,e^b=eg,d^c=dg,e^c=eg,f^c=fg63 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1903, C2×#72023, #10797056, … |
| maximal normal subgroup of | D3×#1903, C2×#72023, #10797056, … |
| maximal quotient of | #10690612, #10690619, #10690640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4599);