Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #1785 |
584 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(5,7)(8,11,13,12)(9,15,16,17)(10,19,20,21)(14,22,18,23);(8,10)(9,14)(11,19)(12,21)(13,20)(15,22)(16,18)(17,23);(2,3)(4,5)(6,7)(8,9,12,17,13,16,11,15)(10,18,19,23,20,14,21,22)Polycyclic presentation:
2^7,3|a^2=f,c^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,f^b=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10682463, #10682464, #10682469, … |
| maximal normal subgroup of | #10682463, #10682464, #10682469, … |
| maximal quotient of | #10686521, #10686525, #10686535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4713);