Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1515 ⋊ C2 |
| Sylow | C53 ⋊ #8503 |
672 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 103 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:
(1,2)(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)(55,61)(57,58)(60,64)(62,63)(65,66)(68,69)(70,73,76,88)(71,78,81,94)(72,83,85,99)(74,89,75,87)(77,90,91,101)(79,95,80,93)(82,96,92,97)(84,100,86,98);(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)(55,60)(57,66)(58,65)(59,67)(61,64)(62,69)(63,68)(70,72)(71,77)(73,83)(74,86)(75,84)(76,85)(78,90)(79,92)(80,82)(81,91)(87,100)(88,99)(89,98)(93,96)(94,101)(95,97);(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)(56,64,66,68,67,69,65,60)(70,71,75,80,76,81,74,79)(72,82,86,77,85,92,84,91)(73,78,87,93,88,94,89,95)(83,97,98,101,99,96,100,90)Polycyclic presentation:
2^8,53|a^2=f,c^2=gh,d^2=h,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^52,d^b=dh,e^b=eh,f^b=fgh,i^b=i^52,d^c=dh,e^c=eg,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, 61998);