Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#328 ⋊ C2 |
| Sylow | C3 ⋊ #1615 |
208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2)(4,7)(5,10)(6,12)(8,14)(9,15)(11,17)(13,19)(16,18)(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29);(2,3)(4,6)(5,9)(7,12)(8,13)(10,15)(11,16)(14,19)(17,18)(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32);(2,3)(4,5,8,11)(6,9,13,16)(7,10,14,17)(12,18,19,15)(20,21,25,28)(22,29,31,34)(23,27,24,32)(26,33,35,30)Polycyclic presentation:
2^7,3|a^2=fg,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^2,d^b=df,e^b=eg,h^b=h^2,d^c=dg,h^c=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1615, C2×#68330, #10767343, … |
| maximal normal subgroup of | D3×#1615, C2×#68330, #10767343, … |
| maximal quotient of | #10684217, #10684225, #10684293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 906);