Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1852 |
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 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);(4,6,7,5)(13,16)(14,19)(17,18);(2,3)(4,5,7,6)(8,9)(10,11)(12,13)(14,16)(15,18)(17,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,d^b=dg78 conjugacy classes — view the full character table.
| maximal subgroup of | #10689161, #10689162, #10689172, … |
| maximal normal subgroup of | #10689161, #10689162, #10689172, … |
| maximal quotient of | #10689015, #10689032, #10689163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4131);