Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#329 ⋊ C2 |
| Sylow | C3 ⋊ #1662 |
196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 196 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:
(1,2,3)(7,17)(10,15)(12,19)(13,16)(20,22)(21,26)(23,31)(24,33)(25,32)(27,30)(28,35)(29,34);(2,3)(4,6,8,14)(5,9,11,18)(7,16,17,13)(10,19,15,12)(20,22)(21,26)(23,33)(24,31)(25,32)(27,35)(28,30)(29,34);(2,3)(4,5,8,11)(6,12,14,19)(7,15,17,10)(9,16,18,13)(20,21,25,29)(22,30,32,35)(23,28,24,27)(26,33,34,31)Polycyclic presentation:
2^7,3|a^2=f,b^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=efg39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1662, C2×#68358, #10776361, … |
| maximal normal subgroup of | D3×#1662, C2×#68358, #10776361, … |
| maximal quotient of | #10684045, #10684046, #10684094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 934);