Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #8492 |
692 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 107 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) = 3392 |
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)(56,61)(58,60)(62,65)(63,69)(64,73)(66,79)(67,78)(68,81)(70,83)(71,85)(72,86)(74,91)(75,90)(76,84)(77,80)(82,88)(87,93)(89,92);(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)(56,60)(57,59)(58,61)(62,64,67,75)(63,68,70,72)(65,73,78,90)(66,74,80,92)(69,81,83,86)(71,82,84,87)(76,93,85,88)(77,89,79,91);(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)(55,58,59,60)(62,63)(64,72,75,68)(65,76,78,85)(66,71)(67,70)(69,77,83,79)(73,88)(74,87,92,82)(80,84)(81,89)(86,91)(90,93)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,d^2=h,e^2=g,b^a=bd,c^a=ce,d^a=dg,i^a=i^52,d^b=dh,e^b=eh,f^b=fgh,i^b=i^52,d^c=dh,e^c=eg,f^c=fg710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61929);