Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9334 |
398 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 85 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:
(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)(54,57,59,65)(55,60,61,64)(56,63,62,69)(58,67,68,66)(70,73)(71,78)(72,82)(74,86)(75,90)(76,87)(77,91)(79,94)(80,95)(81,96)(83,98)(84,100)(85,89)(88,99)(92,101)(93,97);(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)(54,56,58,61,59,62,68,55)(57,63,67,64,65,69,66,60)(70,72,74,88,76,84,75,83)(71,77,79,92,80,93,89,81)(73,82,86,99,87,100,90,98)(78,91,94,101,95,97,85,96);(54,55,58,62,59,61,68,56)(57,64,66,69,65,60,67,63)(70,71)(72,81,84,92)(73,85)(74,79)(75,89)(76,80)(77,83,93,88)(78,86)(82,97,100,91)(87,94)(90,95)(96,98,101,99)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=g,d^2=gh,e^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,e^b=eg,f^b=fh,d^c=dg,e^c=egh,f^c=fg,i^c=i^52710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66537);