Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ #1484 |
262 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 262 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)(5,10,11,9)(12,15,17,16)(13,18,14,19);(2,3)(5,9)(6,7)(10,11)(12,14)(13,17)(15,19)(16,18);(2,3)(4,5)(6,10)(7,9)(8,11)(12,13,16,19,17,14,15,18)Polycyclic presentation:
2^7,3|a^2=e,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^2,c^b=cfg,d^b=df,h^b=h^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10687039, #10687042, #10687053, … |
| maximal normal subgroup of | #10687039, #10687042, #10687053, … |
| maximal quotient of | #10683612, #10683636, #10683653, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2429);