Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2161 |
140 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 81 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:
(1,2,3)(6,17)(11,26)(15,29)(18,33)(19,20)(25,32)(27,30)(31,34);(2,3)(4,6,16,32,9,20,23,33,10,17,22,25,8,19,7,18)(5,11,21,31,13,27,28,29,14,26,35,34,24,30,12,15);(4,5,8,13,10,14,9,24)(6,15,19,31,17,29,20,34)(7,21,22,28,23,35,16,12)(11,25,27,33,26,32,30,18)Polycyclic presentation:
2^7,3|a^2=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10710613, #10710615, #10710616, … |
| maximal normal subgroup of | #10710613, #10710615, #10710616, … |
| maximal quotient of | #10706774, #10706777, #10706838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3259);