Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#431 ⋊ C2 |
| Sylow | C3 ⋊ #3106 |
434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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)(4,6,7,10)(5,9,8,11);(2,3)(12,14)(13,17)(15,18)(16,19);(5,8)(9,11)(12,13,15,16)(14,17,18,19);(2,3)(4,5)(6,9)(7,8)(10,11)(13,16)(14,17)(18,19)Polycyclic presentation:
2^7,3|b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,f^c=fg,h^c=h^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10689891, #10689893, #10689898, … |
| maximal normal subgroup of | #10689891, #10689893, #10689898, … |
| maximal quotient of | #10795225, #10798171, #10798193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11877);