Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2245 |
132 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3)(5,9)(8,11)(12,15,16,29,33,26,17,28,19,31,35,27,18,30,34,14)(13,21,22,41,37,38,23,40,25,43,36,39,24,42,32,20);(2,3)(4,6,7,10)(5,8,9,11)(12,14,17,26,18,27,16,15,19,28,34,30,33,29,35,31)(13,20,23,38,24,39,22,21,25,40,32,42,37,41,36,43);(4,5)(6,8)(7,9)(10,11)(12,13,19,25)(14,21,28,43)(15,20,31,40)(16,32,35,23)(17,36,34,22)(18,37,33,24)(26,39,30,41)(27,38,29,42)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ceg,d^a=df,e^a=efg,f^a=fg,c^b=cg,h^b=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2245, C2×#69218, #10950507, … |
| maximal normal subgroup of | D3×#2245, C2×#69218, #10950507, … |
| maximal quotient of | #10711571, #10713121, #10713122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1794);