Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#352 ⋊ C2 |
| Sylow | C3 ⋊ #2200 |
260 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 41 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(3,10)(4,12)(6,13)(9,15)(17,18);(1,3,5,10)(2,6,8,13)(4,11,12,16)(7,9,14,15);(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(18,19)Polycyclic presentation:
2^7,3|b^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,c^b=cg,e^b=efg,d^c=df,h^c=h^2,e^d=eg30 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2200, C2×#69139, #10949237, … |
| maximal normal subgroup of | D3×#2200, C2×#69139, #10949237, … |
| maximal quotient of | #10707237, #10707242, #10707271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1715);