Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9006 |
376 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 103 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)(54,57,59,61)(55,56,64,68)(58,65,60,69)(62,67,63,66)(70,73)(71,78)(72,82)(74,88)(75,87)(76,86)(77,90)(79,94)(80,85)(81,93)(83,99)(84,97)(89,98)(91,100)(92,101)(95,96);(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)(55,61)(57,64)(58,67)(59,68)(60,66)(62,69)(63,65)(70,72,75,83,76,84,74,89)(71,77,80,91,81,92,79,95)(73,82,87,99,86,97,88,98)(78,90,85,100,93,101,94,96);(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)(54,55,60,63,59,64,58,62)(56,65,67,61,68,69,66,57)(70,71,75,80,76,81,74,79)(72,77,83,91,84,92,89,95)(73,85,88,78,86,94,87,93)(82,96,98,101,97,100,99,90)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=g,d^2=g,e^2=gh,f^2=h,b^a=bd,c^a=ce,e^a=eg,i^a=i^52,d^b=dg,e^b=eh,f^b=fg,i^b=i^52,d^c=dh,e^c=egh,f^c=fh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 64523);