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 ⋊ #1914 |
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 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)(5,10)(6,13)(8,17)(9,15)(11,14)(12,19)(16,18);(4,6,8,11,9,12,18,5)(7,13,17,14,15,19,16,10);(2,3)(4,5,8,12,9,11,18,6)(7,14,16,19,15,10,17,13)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg63 conjugacy classes — view the full character table.
| maximal subgroup of | #10710958, #10710963, #10710965, … |
| maximal normal subgroup of | #10710958, #10710963, #10710965, … |
| maximal quotient of | #10690722, #10690732, #10691170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4606);