Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×Q8⋊C16 ⋊ C2 |
| Sylow | C53 ⋊ #12385 |
300 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 67 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)(54,56,58,63)(55,59,61,68)(57,67,66,64)(60,69,65,62)(70,73,76,75)(71,78,80,90)(72,82,84,91)(74,85,89,88)(77,93,95,94)(79,86,97,100)(81,98,99,96)(83,87,92,101);(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)(57,66)(60,65)(62,69)(64,67)(70,72)(71,77)(73,82)(74,87)(75,91)(76,84)(78,93)(79,96)(80,95)(81,86)(83,88)(85,92)(89,101)(90,94)(97,98)(99,100);(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)(54,55,58,61)(56,62,63,69)(57,65,66,60)(59,67,68,64)(70,71,76,80)(72,81,84,99)(73,78,75,90)(74,86,89,100)(77,92,95,83)(79,85,97,88)(82,98,91,96)(87,93,101,94)Polycyclic presentation:
2^8,53|a^2=gh,c^2=gh,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,i^a=i^52,d^b=df,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=eg1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83469);