Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#428 ⋊ C2 |
| Sylow | C3 ⋊ #3079 |
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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)(12,14,16,15)(13,17,18,19);(2,3)(12,13)(14,17)(15,19)(16,18);(2,3)(4,6,7,11)(5,8,9,10);(4,5,7,9)(6,10,11,8)(13,17)(14,15)(18,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^2,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10836641, #10836643, #10836652, … |
| maximal normal subgroup of | #10836641, #10836643, #10836652, … |
| maximal quotient of | #10794681, #10796158, #10796165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11816);