Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1561 |
210 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 77 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,8,7)(5,9,10,11)(12,15,17,16)(13,18,14,19);(2,3)(4,5,8,10)(6,9,7,11)(12,14)(13,17)(15,19)(16,18);(5,9)(6,7)(10,11)(12,13,16,18,17,14,15,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=g,d^2=g,e^2=fg,b^a=bd,c^a=cg,d^a=df,d^b=dg,e^b=efg,h^b=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10687419, #10687420, #10687424, … |
| maximal normal subgroup of | #10687419, #10687420, #10687424, … |
| maximal quotient of | #10683287, #10683304, #10683433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3087);