Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2081 |
204 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 59 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,7,16,9,15,8,17)(5,11,12,14,13,19,10,18);(5,10)(6,15)(7,8)(11,18)(12,13)(14,19);(2,3)(4,5,8,10,9,13,7,12)(6,14,16,19,15,18,17,11)Polycyclic presentation:
2^7,3|a^2=e,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg,e^c=eg,f^c=fg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2081, C2×#70078, #10824136, … |
| maximal normal subgroup of | D3×#2081, C2×#70078, #10824136, … |
| maximal quotient of | #10699978, #10699988, #10699995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2654);