Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1531 ⋊ C2 |
| Sylow | C53 ⋊ #9312 |
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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:
(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)(62,65)(63,70)(64,73)(66,80)(67,77)(68,78)(69,82)(71,86)(72,87)(74,89)(75,91)(76,79)(81,90)(83,93)(84,88)(85,92);(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)(55,58,60,59)(62,64,66,75,68,74,67,81)(63,69,72,83,71,85,79,84)(65,73,80,91,78,89,77,90)(70,82,87,93,86,92,76,88);(54,55,56,58,57,60,61,59)(62,63,67,72,68,71,66,79)(64,69,75,84,74,85,81,83)(65,76,77,70,78,87,80,86)(73,88,91,92,89,93,90,82)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=gh,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,f^b=fh,e^c=eh,i^c=i^52881 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66383);