Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C3 ⋊ #2199 |
270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 270 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)(17,18,19);(1,3)(2,6)(4,11)(5,10)(7,9)(8,13)(12,16)(14,15)(18,19);(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(18,19)Polycyclic presentation:
2^7,3|b^a=bd,c^a=ce,f^a=fg,h^a=h^2,c^b=cg,e^b=efg,h^b=h^2,d^c=df,e^d=eg30 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2199, C2×#69131, #10949235, … |
| maximal normal subgroup of | D3×#2199, C2×#69131, #10949235, … |
| maximal quotient of | #10707235, #10707236, #10707275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1707);