Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #12764 |
768 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 points:
(5,8,10,21)(6,12,14,29)(7,16,18,19)(9,20,24,36)(11,25,26,27)(13,31,22,28)(15,32,30,33)(17,34,23,35)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88);(5,7,10,18)(6,11,14,26)(8,19,21,16)(9,23,24,17)(12,27,29,25)(13,30,22,15)(20,34,36,35)(28,33,31,32);(1,2,3,4)(5,6)(7,15,18,30)(8,12)(9,22,24,13)(10,14)(11,17)(16,33,19,32)(20,31,36,28)(21,29)(23,26)(25,34)(27,35)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=h,d^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,c^b=ch,d^b=dh,e^b=egh,f^b=fgh,d^c=dg,i^c=i^52,e^d=eh,f^d=fh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85399);