Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1695 ⋊ C2 |
| Sylow | C53 ⋊ #12400 |
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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)(65,66)(73,86)(77,96)(80,99)(81,91)(84,98)(85,101)(88,94)(95,100);(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)(54,56,59,67)(55,60,63,69)(57,66,58,65)(61,68,62,64)(70,72,75,82)(71,76,79,92)(73,85,86,101)(74,90,87,83)(77,95,96,100)(78,97,89,93)(80,98,99,84)(81,94,91,88);(54,55,59,63)(56,64,67,68)(57,62,58,61)(60,66,69,65)(70,71,75,79)(72,80,82,99)(73,84,86,98)(74,89,87,78)(76,91,92,81)(77,94,96,88)(83,100,90,95)(85,97,101,93)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,d^2=fh,e^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=egh,f^a=fh,d^b=df,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=egh629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83570);