Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1470 ⋊ C2 |
| Sylow | C53 ⋊ #8485 |
630 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 630 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) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 101 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)(54,56,58,63)(55,60,61,69)(57,65,66,62)(59,67,64,68)(70,73)(71,77)(72,81)(74,88)(75,85)(76,90)(78,84)(79,95)(80,96)(82,97)(83,99)(86,89)(87,98)(91,101)(92,93)(94,100);(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)(57,64)(58,61)(59,66)(62,67)(63,69)(65,68)(70,72)(71,76)(73,81)(74,87)(75,82)(77,90)(78,80)(79,94)(83,89)(84,96)(85,97)(86,99)(88,98)(91,93)(92,101)(95,100);(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)(55,59,61,64)(60,68,69,67)(70,71,74,79,75,78,89,93)(72,80,83,94,82,76,87,91)(73,84,86,95,85,77,88,92)(81,96,98,101,97,90,99,100)Polycyclic presentation:
2^8,53|a^2=f,c^2=h,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^52,d^b=dh,e^b=egh,f^b=fgh,i^b=i^52,d^c=dgh,f^c=fg869 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61883);