Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C3 ⋊ #1274 |
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 27 points:
(2,3)(12,14)(13,17,19,24)(15,21)(16,22)(18,20,25,26)(23,27);(1,2,3)(4,5,6,8,7,9,10,11)(12,13)(14,20,22,26)(15,18)(16,19)(17,21,24,27)(23,25)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=f,d^2=g,b^a=bc,e^a=ef,d^b=df,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1274, C2×#67737, #10684584, … |
| maximal normal subgroup of | D3×#1274, C2×#67737, #10684584, … |
| maximal quotient of | C3⋊#7014, #10681718, #10681720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 313);