Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1932 |
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(4,6,7,15,9,16,8,17)(5,11,12,19,13,14,10,18);(1,2,3)(5,10,13,12)(11,18,14,19);(4,5,8,12,9,13,7,10)(6,14,17,18,16,11,15,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^c=eg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1932, C2×#70378, #10797772, … |
| maximal normal subgroup of | D3×#1932, C2×#70378, #10797772, … |
| maximal quotient of | #10693413, #10693420, #10693427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2954);