Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #2238 |
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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:
(2,3)(4,5,7,16,8,10,15,11)(6,14,12,17,13,18,19,9);(1,2,3)(6,13)(9,17)(12,19)(14,18);(5,9)(6,12)(7,15)(10,17)(11,14)(13,19)(16,18)Polycyclic presentation:
2^7,3|c^2=df,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,e^b=eg,d^c=dg,e^c=efg,f^c=fg,h^c=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | #10708512, #10708513, #10708523, … |
| maximal normal subgroup of | #10708512, #10708513, #10708523, … |
| maximal quotient of | #10711512, #10711753, #10712233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3664);