Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4487 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1385 |
124 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 69 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 — 2 generators on 35 points:
(2,3)(4,6,9,20,8,24,23,35,11,21,22,34,10,19,7,18)(5,12,15,28,26,27,13,17,16,30,31,32,14,29,25,33);(1,2,3)(4,5,8,14,11,16,10,26)(6,17,19,32,21,33,24,28)(7,15,9,25,23,31,22,13)(12,20,27,18,30,34,29,35)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,d^b=dg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1385, C2×#67731, #10710485, … |
| maximal normal subgroup of | D3×#1385, C2×#67731, #10710485, … |
| maximal quotient of | #10682062, #10682107, #10682109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 307);