Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68629 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2072 |
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 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) = 384 |
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)(16,17,19,22)(18,20,23,21);(4,5,6,7)(8,9)(10,13)(11,12)(14,15)Polycyclic presentation:
2^7,3|a^2=e,b^2=g,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 | #10684218, #10684219, #10684232, … |
| maximal normal subgroup of | #10684218, #10684219, #10684232, … |
| maximal quotient of | #10699899, #10699904, #10699916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1212);