Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#410 ⋊ C2 |
| Sylow | C3 ⋊ #1795 |
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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)(4,6)(5,10)(7,14)(8,15)(9,17)(11,18)(12,13)(16,19);(2,3)(5,9)(7,16)(10,17)(11,12)(13,18)(14,19);(4,5)(6,13,15,10)(7,9)(8,12)(11,16)(14,18,19,17)Polycyclic presentation:
2^7,3|a^2=f,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,h^b=h^2,f^c=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | #10710731, #10710733, #10710741, … |
| maximal normal subgroup of | #10710731, #10710733, #10710741, … |
| maximal quotient of | #10686605, #10686611, #10686616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2624);