Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1984 |
292 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(16,18,19,23)(17,20,21,22);(5,7)(8,10,12,14,13,9,11,15);(2,3)(4,5,6,7)(8,9,12,15,13,10,11,14)(16,17,19,21)(18,22,23,20)Polycyclic presentation:
2^7,3|a^2=f,b^2=deg,c^2=ef,e^2=g,f^2=g,b^a=bd,c^a=cef,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10681998, #10686592, #10686602, … |
| maximal normal subgroup of | #10681998, #10686592, #10686602, … |
| maximal quotient of | #10695168, #10695172, #10695177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2364);