Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C53×#491 ⋊ C2 |
| Sylow | C53 ⋊ #19060 |
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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 — 4 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)(73,84)(77,92)(81,98)(85,88)(90,101)(93,95)(96,97)(99,100);(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)(54,56)(55,59)(57,66)(58,63)(60,69)(61,68)(62,64)(65,67)(70,73)(71,77)(72,81)(74,88)(75,84)(76,90)(78,95)(79,92)(80,96)(82,100)(83,98)(85,89)(86,93)(87,99)(91,101)(94,97);(54,55,58,61)(56,59,63,68)(57,65,64,60)(62,69,66,67)(70,72,75,83)(71,76,79,91)(73,81,84,98)(74,87,89,82)(77,90,92,101)(78,94,86,80)(85,100,88,99)(93,96,95,97);(56,62)(57,64)(59,67)(60,65)(63,66)(68,69)(70,71,75,79)(72,80,83,94)(73,77,84,92)(74,86,89,78)(76,87,91,82)(81,97,98,96)(85,95,88,93)(90,100,101,99)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,e^2=g,f^2=gh,b^a=be,c^a=cf,e^a=eg,f^a=fgh,e^b=eg,f^b=fh,d^c=dg,e^c=eh,f^c=fgh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 151443);