Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1458 |
264 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 109 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 — 3 generators on 27 points:
(1,2,3)(12,15,16,23)(13,18,19,25)(14,21,22,27)(17,24,20,26);(12,14)(13,17)(15,21)(16,22)(18,24)(19,20)(23,27)(25,26);(2,3)(4,5,6,8,7,9,10,11)(12,13)(14,20,22,17)(15,18)(16,19)(21,26,27,24)(23,25)Polycyclic presentation:
2^7,3|a^2=e,c^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^2,e^b=ef84 conjugacy classes — view the full character table.
| maximal subgroup of | #10682147, #10682148, #10682151, … |
| maximal normal subgroup of | #10682147, #10682148, #10682151, … |
| maximal quotient of | #10683126, #10683134, #10683181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4147);