Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ #1913 |
380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 85 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)(4,7)(5,10)(6,12)(8,15)(9,16)(11,14)(13,18)(17,19);(2,3)(4,6)(5,9,11,17)(7,12)(8,13)(10,16,14,19)(15,18);(4,5)(6,9,13,17)(7,14,15,10)(8,11)(12,16)(18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,e^b=eg,f^b=fg,h^b=h^2,d^c=dg,f^c=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | #10710945, #10710948, #10710952, … |
| maximal normal subgroup of | #10710945, #10710948, #10710952, … |
| maximal quotient of | #10690720, #10690725, #10690730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2600);