Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2264 ⋊ C2 |
| Sylow | C53 ⋊ #33981 |
466 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)(54,57,60,75)(55,63,62,66)(56,68,72,71)(58,73,79,106)(59,74,82,107)(61,84,83,93)(64,88,86,91)(65,89,87,80)(67,95,94,102)(69,96,99,98)(70,97,101,81)(76,103,108,109)(77,104,111,110)(78,105,112,116)(85,92,113,115)(90,100,114,117);(55,62)(61,83)(63,66)(64,86)(65,87)(67,94)(76,108)(80,89)(84,93)(85,113)(88,91)(90,114)(92,115)(95,102)(100,117)(103,109);(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)(55,61)(57,68)(58,77)(59,81)(60,72)(62,83)(63,84)(64,90)(65,92)(66,93)(67,76)(69,78)(70,74)(71,75)(73,104)(79,111)(80,85)(82,97)(86,114)(87,115)(88,100)(89,113)(91,117)(94,108)(95,103)(96,105)(98,116)(99,112)(101,107)(102,109)(106,110);(54,55)(56,67)(57,63)(58,76)(59,80)(60,62)(61,69)(64,78)(65,74)(66,75)(68,95)(70,100)(71,102)(72,94)(73,103)(77,92)(79,108)(81,90)(82,89)(83,99)(84,96)(85,110)(86,112)(87,107)(88,105)(91,116)(93,98)(97,114)(101,117)(104,113)(106,109)(111,115)Polycyclic presentation:
2^8,53|d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=be,c^a=ch,e^a=ef,f^a=fg,g^a=gh,e^b=ef,f^b=fg,g^b=gh,i^b=i^52,i^d=i^52728 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 327713);