Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #11369 |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61,69,84,63,75,62,74)(59,65,77,87,67,73,66,81)(60,70,71,85,72,86,76,88)(64,78,68,83,79,80,82,89);(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)(58,60,69,71,63,72,62,76)(59,64,77,68,67,79,66,82)(61,70,84,85,75,86,74,88)(65,80,87,89,73,78,81,83);(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)(54,55,56,57)(58,59)(60,68,72,82)(61,73)(62,66)(63,67)(64,71,79,76)(65,75)(69,77)(70,83,86,89)(74,87)(78,85,80,88)(81,84)Polycyclic presentation:
2^8,53|a^2=g,b^2=de,c^2=de,d^2=h,b^a=bd,c^a=ce,f^a=fh,i^a=i^52,c^b=cf,d^b=dh,e^b=eh,g^b=gh,i^b=i^52,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78424);