Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1360 ⋊ C2 |
| Sylow | C53 ⋊ #11943 |
306 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 101 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)(54,57,59,58)(55,61,62,63)(56,65,66,67)(60,68,64,69);(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)(54,56)(55,60)(57,65)(58,67)(59,66)(61,68)(62,64)(63,69)(70,72)(71,77)(73,87)(74,83)(75,91)(76,86)(78,95)(79,82)(80,99)(81,94)(84,89)(85,88)(90,101)(92,97)(93,96)(98,100);(54,55,58,63,59,62,57,61)(56,64,65,69,66,60,67,68)(70,71,74,79,75,80,89,97,76,81,90,98,88,96,73,78)(72,82,84,94,85,95,83,99,86,100,87,77,91,92,101,93)Polycyclic presentation:
2^8,53|a^2=e,c^2=f,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, 80870);