Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1363 ⋊ C2 |
| Sylow | C53 ⋊ #11934 |
306 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 95 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)(62,65,69,68)(63,71,75,74)(64,77,80,84)(66,81,83,67)(70,85,87,91)(72,88,90,73)(76,89,92,86)(78,82,93,79);(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)(54,55,57,59)(56,61,60,58)(62,64)(63,70)(65,77)(66,82)(67,78)(68,84)(69,80)(71,85)(72,89)(73,76)(74,91)(75,87)(79,83)(81,93)(86,90)(88,92);(55,58)(56,60)(59,61)(62,63,67,73,68,74,83,90,69,75,81,88,65,71,66,72)(64,76,79,87,77,89,78,91,80,92,82,70,84,86,93,85)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=h,d^2=gh,e^2=fg,g^2=h,b^a=bd,d^a=df,d^b=dg,e^b=efg,g^b=gh,i^c=i^52812 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80832);