Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4487 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2155 |
144 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 144 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)(4,7,10,9)(5,12,14,24)(6,16,18,19)(8,20,23,22)(11,25,26,35)(13,21,27,34)(15,28,29,33)(17,30,31,32);(2,3)(4,6,8,17,9,19,22,32,10,18,23,31,7,16,20,30)(5,11,13,15,12,25,21,28,14,26,27,29,24,35,34,33);(4,5)(6,15,18,29)(7,12)(8,21)(9,24)(10,14)(11,17,26,31)(13,22)(16,28,19,33)(20,27)(23,34)(25,30,35,32)Polycyclic presentation:
2^7,3|a^2=e,b^2=d,c^2=g,d^2=f,f^2=g,b^a=bd,d^a=df,f^a=fg,e^b=eg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10710565, #10710568, #10710613, … |
| maximal normal subgroup of | #10710565, #10710568, #10710613, … |
| maximal quotient of | #10706741, #10706746, #10706820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3226);