Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C23×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ #1869 |
432 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 432 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) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(9,11);(5,7)(12,14,15,19,16,13,17,18);(2,3)(4,5,6,7)(8,9)(10,11)(12,13,15,18,16,14,17,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,f^2=g,b^a=bd,c^a=ce,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10686579, #10686582, #10686719, … |
| maximal normal subgroup of | #10686579, #10686582, #10686719, … |
| maximal quotient of | #10689708, #10689713, #10689718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4551);