Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1299 |
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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 — 2 generators on 19 points:
(2,3)(4,5,6,9,7,8,10,11)(13,17,19,18);(1,2,3)(5,8)(6,10)(12,13,15,18,16,19,14,17)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=f,d^2=f,e^2=g,b^a=bc,c^a=cf,e^a=efg,c^b=cg,h^b=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1299, C2×#67710, #10685349, … |
| maximal normal subgroup of | D3×#1299, C2×#67710, #10685349, … |
| maximal quotient of | #10681740, #10681751, #10681754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 286);