Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1867 |
374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(8,10)(9,12)(11,14)(13,15);(2,3)(4,6,7,5)(8,9)(10,12)(11,13)(14,15);(2,3)(4,5,7,6)(12,15)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,b^a=bd,c^a=ce,h^a=h^2,e^b=eg,h^b=h^2,d^c=dg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10711942, #10711943, #10711949, … |
| maximal normal subgroup of | #10711942, #10711943, #10711949, … |
| maximal quotient of | #10689155, #10689160, #10689165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2597);