Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68807 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2043 |
298 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 87 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) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(5,7)(8,10,11,9)(13,17)(14,18)(15,19);(8,9)(10,11)(12,14,16,13)(15,18,19,17);(2,3)(4,5)(6,7)(9,10)(12,13,16,14)(15,17,19,18)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,e^b=eg,f^b=fg,e^c=eg,f^c=fg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2043, C2×#70284, #10822873, … |
| maximal normal subgroup of | D3×#2043, C2×#70284, #10822873, … |
| maximal quotient of | #10698533, #10698538, #10698585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2860);