Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 113 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)(4,7,8,18,9,19,20,31)(5,11,12,24,13,25,26,34)(6,15,17,30,16,29,21,32)(10,22,23,33,14,27,28,35);(2,3)(4,6)(5,10,13,14)(7,15)(8,17)(9,16)(11,22,25,27)(12,23,26,28)(18,30)(19,29)(20,21)(24,33,34,35)(31,32);(2,3)(4,5,8,12,9,13,20,26)(6,14,17,28,16,10,21,23)(7,11,18,24,19,25,31,34)(15,27,30,35,29,22,32,33)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,h^a=h^2,d^b=dg,h^b=h^2,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10710340, #10710342, #10710345, … |
| maximal normal subgroup of | #10710340, #10710342, #10710345, … |
| maximal quotient of | #10685717, #10685721, #10685725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2709);