Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1826 |
306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 306 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) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(4,6,7,10)(5,9,8,11)(12,14)(13,16)(15,17)(18,19);(5,8)(9,11);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13,15,18,16,14,19,17)Polycyclic presentation:
2^7,3|a^2=f,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,e^c=eg,h^c=h^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10686772, #10686773, #10686782, … |
| maximal normal subgroup of | #10686772, #10686773, #10686782, … |
| maximal quotient of | #10688535, #10688539, #10688544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2018);