Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #10217 |
430 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 81 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)(54,57,59,55)(56,63,65,69)(58,68,60,62)(61,64,67,66)(70,73)(71,78)(72,82)(74,89)(75,88)(76,87)(77,91)(79,96)(80,85)(81,95)(83,99)(84,98)(86,90)(92,101)(93,100)(94,97);(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)(54,56,59,65)(55,61,57,67)(58,66,60,64)(62,69,68,63)(70,72)(71,77)(73,86)(74,83)(75,90)(76,84)(78,94)(79,92)(80,97)(81,93)(82,89)(85,100)(87,99)(88,98)(91,96)(95,101);(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)(56,63)(57,59)(58,68)(60,62)(61,64)(65,69)(66,67)(70,71,76,81)(72,77,84,93)(73,85,87,96)(74,80,75,79)(78,89,95,88)(82,94,98,101)(83,97,90,92)(86,91,99,100)Polycyclic presentation:
2^8,53|a^2=h,b^2=g,c^2=g,d^2=g,e^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^a=fh,i^a=i^52,c^b=cf,d^b=dg,f^b=fgh,i^b=i^52,d^c=dh,e^c=eh,f^c=fgh,i^c=i^52704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 71800);