Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1905 ⋊ C2 |
| Sylow | C53 ⋊ #30443 |
854 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 117 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)(54,58)(55,64)(56,70)(57,76)(59,84)(60,82)(61,83)(62,86)(63,90)(65,95)(66,94)(67,80)(68,96)(69,97)(71,101)(72,81)(73,100)(74,103)(75,105)(77,107)(78,106)(79,108)(85,111)(87,93)(88,112)(89,113)(91,114)(92,109)(98,110)(99,116)(102,117)(104,115);(54,57)(55,63)(56,69)(58,76)(59,77)(60,78)(61,79)(62,85)(64,90)(65,91)(66,74)(67,92)(68,89)(70,97)(71,75)(72,98)(73,99)(80,109)(81,110)(82,106)(83,108)(84,107)(86,111)(87,104)(88,102)(93,115)(94,103)(95,114)(96,113)(100,116)(101,105)(112,117);(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)(54,56,61,73)(55,62,67,88)(57,75,79,98)(58,81,83,101)(59,72,60,71)(63,89,92,104)(64,93,80,96)(65,87,66,68)(69,78,99,77)(70,84,100,82)(74,102,91,85)(76,97,108,116)(86,95,112,94)(90,111,109,117)(103,113,114,115)(105,107,110,106);(54,55,61,67)(56,68,73,87)(57,74,79,91)(58,80,83,64)(59,66,60,65)(62,72,88,71)(63,77,92,78)(69,85,99,102)(70,93,100,96)(75,104,98,89)(76,103,108,114)(81,86,101,112)(82,94,84,95)(90,107,109,106)(97,111,116,117)(105,115,110,113)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,f^a=fh,g^a=gh,c^b=cg,d^b=de,e^b=eh,f^b=fh,g^b=gh,i^b=i^52,f^c=fh,g^c=gh,e^d=eh,f^d=fh,i^d=i^52788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 284102);