Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3167 |
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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)(12,13,14,16,15,17,18,19);(5,8)(9,11);(4,5)(6,9)(7,8)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10690412, #10690418, #10690420, … |
| maximal normal subgroup of | #10690412, #10690418, #10690420, … |
| maximal quotient of | #10795716, #10799390, #10800360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15866);