Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2031 |
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 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)(4,6)(5,10)(7,14)(8,16)(9,15)(11,19)(12,18)(13,17);(2,3)(6,14,15,16)(10,13,18,19);(4,5)(6,13,15,19)(7,11)(8,17)(9,12)(10,16,18,14)Polycyclic presentation:
2^7,3|a^2=d,b^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,h^b=h^2,d^c=dg,e^c=eg,f^c=fg48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2031, C2×#70394, #10822615, … |
| maximal normal subgroup of | D3×#2031, C2×#70394, #10822615, … |
| maximal quotient of | #10698273, #10698278, #10698283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2970);