Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#390 ⋊ C2 |
| Sylow | C3 ⋊ #2054 |
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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)(5,7)(9,11)(12,14,15,13,17,18,16,19);(8,9)(10,11)(12,13)(14,15)(16,18)(17,19);(2,3)(4,5)(6,7)(13,18)(14,19)(15,16)Polycyclic presentation:
2^7,3|c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2054, C2×#69650, #10823135, … |
| maximal normal subgroup of | D3×#2054, C2×#69650, #10823135, … |
| maximal quotient of | #10698976, #10698978, #10698983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2226);