Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#353 ⋊ C2 |
| Sylow | C3 ⋊ #2196 |
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 11 points:
(3,7)(9,10);(2,5)(6,8)(10,11);(1,2)(3,5)(4,6)(7,8)(10,11)Polycyclic presentation:
2^7,3|b^a=bd,c^a=ce,f^a=fg,h^a=h^2,e^b=efg,h^b=h^2,d^c=df,h^c=h^2,e^d=eg33 conjugacy classes — view the full character table.
| maximal subgroup of | #10715899, #10715900, #10715904, … |
| maximal normal subgroup of | #10715899, #10715900, #10715904, … |
| maximal quotient of | #10707217, #10707252, #10707390, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1722);