Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#431 ⋊ C2 |
| Sylow | C3 ⋊ #3227 |
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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 — 4 generators on 19 points:
(1,2,3)(5,10)(9,11);(2,3)(5,9)(6,8)(10,11)(12,13,15,17)(14,19,18,16);(4,6,7,8)(5,9,10,11);(2,3)(4,5)(6,11)(7,10)(8,9)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=e,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^2,c^b=ce,f^c=fg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10691703, #10691705, #10691829, … |
| maximal normal subgroup of | #10691703, #10691705, #10691829, … |
| maximal quotient of | #10804676, #10804860, #10805702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11845);