Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2050 |
266 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 67 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:
(2,3)(4,7,8,10,9,13,18,19)(5,6,11,14,12,15,16,17);(1,2,3)(4,6)(5,10)(7,11)(8,17)(9,15)(12,19)(13,16)(14,18);(4,5)(6,13)(7,15)(8,16)(9,12)(10,14)(11,18)(17,19)Polycyclic presentation:
2^7,3|c^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,c^b=cf,d^b=dg,e^b=eg,e^c=eg,f^c=fg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10707711, #10707716, #10707721, … |
| maximal normal subgroup of | #10707711, #10707716, #10707721, … |
| maximal quotient of | #10698862, #10698869, #10698876, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4693);