Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9369 |
390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 99 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) = 3392 |
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)(55,60)(57,65)(58,63)(59,67)(61,68)(62,69)(64,66)(70,73)(71,77)(72,81)(74,88)(75,86)(76,90)(78,93)(79,84)(80,94)(82,98)(83,97)(85,89)(87,92)(91,100)(95,101)(96,99);(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)(55,59,61,69)(57,65)(58,63)(60,67,68,62)(64,66)(70,72,74,82,75,83,89,99)(71,76,78,80,79,91,87,95)(73,81,88,98,86,97,85,96)(77,90,93,94,84,100,92,101);(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)(56,59,63,69)(57,62)(58,61)(60,64,68,65)(66,67)(70,71)(72,80)(73,84,86,77)(74,87)(75,79)(76,82)(78,89)(81,94,97,101)(83,95)(85,92,88,93)(90,96,100,98)(91,99)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,d^2=gh,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^52,d^b=dh,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=eh,f^c=fg713 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66787);