Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1946 |
200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 200 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) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(8,11,12,19,13,21,22,10)(9,15,16,20,18,14,17,23);(2,3)(5,7)(8,10,12,11,13,19,22,21)(9,14,17,20,18,15,16,23);(2,3)(4,5)(6,7)(8,9,12,17,13,18,22,16)(10,14,11,20,19,15,21,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,c^2=e,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,c^b=cg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10711843, #10711844, #10711927, … |
| maximal normal subgroup of | #10711843, #10711844, #10711927, … |
| maximal quotient of | #10693735, #10693740, #10693745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3239);