Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1376 |
148 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 23 points:
(2,3)(4,5,6,7)(9,14,17,15)(16,21,23,22);(1,2,3)(8,9,11,16,12,15,19,22,13,17,20,23,10,14,18,21)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=cg,e^a=eg,h^b=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1376, C2×#67810, #10710041, … |
| maximal normal subgroup of | D3×#1376, C2×#67810, #10710041, … |
| maximal quotient of | #10682018, #10682030, #10682037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 386);