Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1808 |
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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)(9,11);(2,3)(12,13,17,19,15,18,14,16);(4,5,6,7)(8,9)(10,11)(13,16)(14,17)(18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=dg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10688083, #10688084, #10688087, … |
| maximal normal subgroup of | #10688083, #10688084, #10688087, … |
| maximal quotient of | #10688024, #10688037, #10688083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2088);