Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68629 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ #2071 |
274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 274 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) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(5,7)(8,10,11,14)(9,13,12,15)(17,20)(18,23)(21,22);(2,3)(9,12)(13,15)(16,17)(18,20)(19,22)(21,23);(4,5,6,7)(8,9)(10,13)(11,12)(14,15)Polycyclic presentation:
2^7,3|a^2=e,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^2,f^c=fg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10684211, #10684212, #10684217, … |
| maximal normal subgroup of | #10684211, #10684212, #10684217, … |
| maximal quotient of | #10699889, #10699894, #10699909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1211);