Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1491 |
252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 252 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) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(5,8)(9,11)(12,15,17,16)(13,18,14,19);(2,3)(12,14,17,13)(15,18,16,19);(4,5,6,9,7,8,10,11)(12,13,16,18,17,14,15,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=f,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=df,h^b=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10686812, #10686816, #10686817, … |
| maximal normal subgroup of | #10686812, #10686816, #10686817, … |
| maximal quotient of | #10683332, #10683336, #10683341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3378);