Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#509 ⋊ C2 |
| Sylow | C3 ⋊ #3415 |
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3)(6,15)(11,25)(16,28)(17,29)(22,33)(26,34)(27,31)(30,35);(2,3)(4,6)(5,11)(7,16)(8,17)(9,15)(10,22)(12,26)(13,27)(14,25)(18,30)(19,29)(20,28)(21,31)(23,34)(24,33)(32,35);(5,10)(7,18)(8,19)(11,22)(12,13)(14,24)(16,30)(17,29)(20,32)(21,23)(25,33)(26,27)(28,35)(31,34);(2,3)(4,5)(6,11)(7,10)(8,21)(9,14)(12,18)(13,19)(15,25)(16,22)(17,31)(20,24)(23,32)(26,30)(27,29)(28,33)(34,35)Polycyclic presentation:
2^7,3|e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^2,e^b=ef,f^b=fg,d^c=dg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10951928, #10951931, #10951936, … |
| maximal normal subgroup of | #10951928, #10951931, #10951936, … |
| maximal quotient of | #10948097, #10948098, #10948230, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14612);