Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#413 ⋊ C2 |
| Sylow | C3 ⋊ #2132 |
250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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)(4,6,9,8)(5,11,14,13)(7,15,16,17)(10,18,12,19);(2,3)(5,10)(7,16)(11,18)(12,14)(13,19)(15,17);(4,5,8,13,9,14,6,11)(7,12,15,19,16,10,17,18)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,d^2=g,e^2=g,b^a=bd,d^a=df,f^a=fg,d^b=dg,e^b=efg,h^b=h^2,e^d=eg48 conjugacy classes — view the full character table.
| maximal subgroup of | #10710380, #10710382, #10710385, … |
| maximal normal subgroup of | #10710380, #10710382, #10710385, … |
| maximal quotient of | #10704291, #10704343, #10704455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2724);