Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×#341 ⋊ C2 |
| Sylow | C3 ⋊ #1937 |
230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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)(5,7)(8,10,11,19,13,21,12,20)(9,15,16,18,17,23,14,22);(2,3)(9,14,17,16)(15,22,23,18);(4,5)(6,7)(8,9,12,16,13,17,11,14)(10,18,20,23,21,22,19,15)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1937, C2×#68918, #10797933, … |
| maximal normal subgroup of | D3×#1937, C2×#68918, #10797933, … |
| maximal quotient of | #10693442, #10693449, #10693484, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1494);