Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1827 |
262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 262 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)(4,6)(5,10,11,17)(7,14)(8,15)(9,12,13,18)(16,19);(4,6)(5,9)(7,14)(8,15)(10,12)(11,13)(16,19)(17,18);(2,3)(4,5)(6,13,15,9)(7,12)(8,11)(10,14,17,19)(16,18)Polycyclic presentation:
2^7,3|a^2=f,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,f^b=fg,f^c=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10710772, #10710774, #10710777, … |
| maximal normal subgroup of | #10710772, #10710774, #10710777, … |
| maximal quotient of | #10688631, #10688635, #10688639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4220);