Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9007 |
502 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(57,59)(60,61)(62,65)(63,70)(64,74)(66,80)(67,79)(68,78)(69,82)(71,86)(72,77)(73,85)(75,91)(76,89)(81,90)(83,92)(84,93)(87,88);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,56,58,55)(57,60,59,61)(62,64,67,75,68,76,66,81)(63,69,72,83,73,84,71,87)(65,74,79,91,78,89,80,90)(70,82,77,92,85,93,86,88);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55,59,61,58,56,57,60)(62,63,67,72,68,73,66,71)(64,69,75,83,76,84,81,87)(65,77,80,70,78,86,79,85)(74,88,90,93,89,92,91,82)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=g,e^2=gh,f^2=h,b^a=bd,c^a=ce,e^a=eg,i^a=i^52,d^b=dg,e^b=eh,f^b=fg,i^b=i^52,d^c=dh,e^c=egh,f^c=fh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 64528);