Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2127 |
286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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)(6,13)(9,18)(12,19)(14,16);(4,6)(5,9)(7,16)(8,13)(10,19)(11,18)(12,15)(14,17);(2,3)(4,5)(6,12,13,19)(7,15,17,10)(8,11)(9,14)(16,18)Polycyclic presentation:
2^7,3|a^2=e,d^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,c^b=cg,d^b=dg,e^b=efg,e^d=eg45 conjugacy classes — view the full character table.
| maximal subgroup of | #10710719, #10710721, #10710722, … |
| maximal normal subgroup of | #10710719, #10710721, #10710722, … |
| maximal quotient of | #10704297, #10704349, #10704473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4436);