Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#380 ⋊ C2 |
| Sylow | C3 ⋊ #1893 |
432 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 121 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(9,11);(2,3)(4,6,7,5)(12,13,17,19,15,18,14,16);(4,5,7,6)(8,9)(10,11)(13,16)(14,17)(18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10686716, #10686720, #10686728, … |
| maximal normal subgroup of | #10686716, #10686720, #10686728, … |
| maximal quotient of | #10690521, #10690541, #10690750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2091);