Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#3139 ⋊ C2 |
| Sylow | C53 ⋊ #19005 |
820 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 820 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)(70,74,76,75)(71,79,81,80)(72,84,85,88)(73,86,87,89)(77,82,91,94)(78,92,93,95)(83,98,100,99)(90,96,101,97);(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)(71,78)(72,83)(74,86)(75,89)(76,87)(77,90)(79,92)(80,95)(81,93)(82,96)(84,98)(85,100)(88,99)(91,101)(94,97);(54,55,58,61)(56,59,63,68)(57,65,64,60)(62,69,66,67)(70,72,76,85)(71,77,81,91)(73,83,87,100)(74,84,75,88)(78,90,93,101)(79,82,80,94)(86,98,89,99)(92,96,95,97);(56,62)(57,64)(59,67)(60,65)(63,66)(68,69)(70,71,76,81)(72,82,85,94)(73,78,87,93)(74,80,75,79)(77,88,91,84)(83,97,100,96)(86,95,89,92)(90,98,101,99)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,d^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fgh,e^b=eg,f^b=fh,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, 150884);