Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1326 |
158 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 37 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) = 96 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2)(13,16,17,18)(14,19);(2,3)(4,5,6,8,7,9,10,11)(12,13)(14,18,19,16)(15,17)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=cg,d^b=de,h^b=h^2,d^c=dg48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1326, C2×#67447, #10704360, … |
| maximal normal subgroup of | D3×#1326, C2×#67447, #10704360, … |
| maximal quotient of | #10681827, #10681834, #10681982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 23);