Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #1851 |
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 105 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:
(2,3)(9,11)(13,17)(14,18);(1,2,3)(5,7)(12,14,16,17,15,18,19,13);(4,5)(6,7)(8,9)(10,11)(12,13,16,14,15,17,19,18)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1851, C2×#70478, #10795851, … |
| maximal normal subgroup of | D3×#1851, C2×#70478, #10795851, … |
| maximal quotient of | #10689030, #10689035, #10689040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3054);