Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13430 |
418 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,3,4,14,6,13,16,28)(2,8,9,22,11,23,7,20)(5,18,17,32,19,15,31,30)(10,25,24,29,26,12,21,27)(33,34)(35,36)(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);(2,7)(3,13)(4,16)(8,20)(9,11)(10,21)(12,27)(17,31)(22,23)(24,26)(25,29)(30,32);(1,2,6,11)(3,12,13,25)(4,7,16,9)(5,10,19,26)(8,18,23,15)(14,29,28,27)(17,21,31,24)(20,32,22,30)(34,35)(36,37)(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)Polycyclic presentation:
2^8,53|a^2=h,c^2=d,d^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fgh,i^a=i^52,c^b=cf,d^b=dh,e^b=eg,e^c=eh,f^c=fh,g^c=gh,i^c=i^52,f^e=fh626 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89052);