Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ #1923 |
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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)(5,7)(8,10,11,9);(2,3)(8,9,11,10)(12,14,15,19,16,13,17,18);(4,5)(6,7)(9,10)(12,13,15,18,16,14,17,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=d,f^2=g,b^a=bd,c^a=ce,h^b=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1923, C2×#68657, #10797475, … |
| maximal normal subgroup of | D3×#1923, C2×#68657, #10797475, … |
| maximal quotient of | #10693358, #10693365, #10693372, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1233);