Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2091 |
222 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 222 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(5,10)(11,17);(4,6,13,14,8,15,7,16)(5,9,17,12,10,18,11,19);(2,3)(4,5,7,11,8,10,13,17)(6,12,14,18,15,19,16,9)Polycyclic presentation:
2^7,3|a^2=d,b^2=de,d^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682783, #10682785, #10682786, … |
| maximal normal subgroup of | #10682783, #10682785, #10682786, … |
| maximal quotient of | #10700156, #10700158, #10700160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2563);