Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9335 |
400 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 95 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)(55,61)(57,58)(60,68)(62,63)(64,69)(65,67)(70,73)(71,77)(72,81)(74,88)(75,85)(76,89)(78,84)(79,95)(80,86)(82,96)(83,98)(87,97)(90,101)(91,99)(92,93)(94,100);(54,56)(55,60,63,69)(57,65)(58,67)(59,66)(61,68,62,64)(70,72,80,83,75,82,74,87)(71,76,79,94,78,91,93,90)(73,81,86,98,85,96,88,97)(77,89,95,100,84,99,92,101);(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)(54,55,57,61,59,63,58,62)(56,64,65,60,66,68,67,69)(70,71,74,79,75,78,80,93)(72,76,83,90,82,91,87,94)(73,84,86,95,85,77,88,92)(81,89,97,100,96,99,98,101)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=gh,e^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^52,d^b=dh,e^b=eg,f^b=fh,d^c=dg,e^c=egh,f^c=fg1022 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66547);