Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1664 |
184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2)(4,6)(5,10)(7,15)(8,17)(9,16)(11,14)(12,19)(13,18)(20,22,24,29)(21,25,27,34)(23,32,30,28)(26,35,31,33);(2,3)(4,6)(5,10)(7,17)(8,15)(9,16)(11,19)(12,14)(13,18)(20,21,24,27)(22,25,29,34)(23,31,30,26)(28,35,32,33);(2,3)(4,5,9,13)(6,14,16,19)(7,12,8,11)(10,17,18,15)(22,28)(23,30)(25,33)(26,31)(29,32)(34,35)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=g,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,h^a=h^2,d^b=df,e^b=eg,h^b=h^2,d^c=dg,e^c=efg,h^c=h^239 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1664, C2×#68359, #10776361, … |
| maximal normal subgroup of | D3×#1664, C2×#68359, #10776361, … |
| maximal quotient of | #10684060, #10684066, #10684073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 935);