Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#361 ⋊ C2 |
| Sylow | C3 ⋊ #2213 |
170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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:
(1,2)(4,6)(5,11)(7,14)(8,16)(9,17)(10,15)(12,19)(13,18);(2,3)(4,5,9,12,10,13,7,8)(6,11,17,19,15,18,14,16);(5,8)(6,11)(7,9)(12,13)(14,19)(15,18)(16,17)Polycyclic presentation:
2^7,3|b^2=dg,d^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^b=h^2,e^c=ef,f^c=fg,h^c=h^239 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2213, C2×#69263, #10949575, … |
| maximal normal subgroup of | D3×#2213, C2×#69263, #10949575, … |
| maximal quotient of | #10709316, #10709320, #10709323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1839);