Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68629 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ #2041 |
402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(5,7)(8,10,11,9)(12,13)(14,18)(15,17)(16,19);(2,3)(8,9)(10,11)(13,18)(14,15)(17,19);(2,3)(4,5)(6,7)(9,10)(13,17)(14,15)(18,19)Polycyclic presentation:
2^7,3|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,h^b=h^2,e^c=eg,f^c=fg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10683891, #10683892, #10683897, … |
| maximal normal subgroup of | #10683891, #10683892, #10683897, … |
| maximal quotient of | #10698512, #10698517, #10698548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1205);