Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2069 |
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 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)(6,14)(7,13)(10,17)(12,18);(4,6,13,19,8,14,7,15)(5,9,10,12,11,16,17,18);(2,3)(4,5,7,10,8,11,13,17)(6,12,15,16,14,18,19,9)Polycyclic presentation:
2^7,3|a^2=d,b^2=de,d^2=g,b^a=bde,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,f^b=fg,d^c=dg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2069, C2×#70077, #10823910, … |
| maximal normal subgroup of | D3×#2069, C2×#70077, #10823910, … |
| maximal quotient of | #10699812, #10699814, #10699816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2653);