Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #3044 |
458 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3)(10,19)(14,28)(18,33)(20,35)(27,38)(29,36)(32,39)(34,37);(2,3)(8,11,13,23)(9,15,17,30)(10,18,19,33)(12,25,26,22)(14,27,28,38)(16,31,24,21)(20,37,35,34)(29,39,36,32);(2,3)(4,5,6,7)(8,10)(9,14)(11,18)(12,20)(13,19)(15,27)(16,29)(17,28)(21,32)(22,34)(23,33)(24,36)(25,37)(26,35)(30,38)(31,39);(2,3)(5,7)(8,9,13,17)(10,14,19,28)(11,21,23,31)(12,24,26,16)(15,25,30,22)(18,32,33,39)(20,36,35,29)(27,37,38,34)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^b=dg,h^b=h^2,f^c=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10832600, #10832607, #10843085, … |
| maximal normal subgroup of | #10832600, #10832607, #10843085, … |
| maximal quotient of | #10780524, #10780533, #10780542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11441);