Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1544 ⋊ C2 |
| Sylow | C53 ⋊ #8478 |
656 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 111 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:
(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)(54,57,59,56)(55,61,62,60)(58,64,66,65)(63,67,69,68)(70,73,75,86)(71,77,79,84)(72,81,83,98)(74,89,90,85)(76,91,92,100)(78,95,87,93)(80,96,94,101)(82,99,88,97);(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)(54,56,59,57)(55,60,62,61)(58,65,66,64)(63,68,69,67)(70,72,75,83)(71,76,79,92)(73,81,86,98)(74,88,90,82)(77,91,84,100)(78,94,87,80)(85,99,89,97)(93,96,95,101);(54,55,58,63,59,62,66,69)(56,61,64,68,57,60,65,67)(70,71)(72,80)(73,84,86,77)(74,87)(75,79)(76,82)(78,90)(81,96,98,101)(83,94)(85,93,89,95)(88,92)(91,97,100,99)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=g,d^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=eh,f^b=fgh,d^c=dh,f^c=fg,i^c=i^521028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61831);