Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2145 ⋊ C2 |
| Sylow | C53 ⋊ #12745 |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(55,62)(56,67)(58,77)(59,74)(60,73)(61,83)(63,89)(64,71)(65,87)(66,92)(68,97)(69,95)(70,96)(72,80)(75,102)(76,108)(78,104)(79,111)(81,101)(82,106)(84,114)(85,100)(86,90)(88,117)(91,116)(93,113)(94,98)(99,115)(103,109)(105,112)(107,110);(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)(57,67)(58,76)(59,82)(60,69)(62,83)(63,88)(64,85)(65,91)(66,75)(68,79)(70,78)(71,100)(72,103)(73,95)(74,106)(77,108)(80,109)(81,84)(86,115)(87,116)(89,117)(90,99)(92,102)(93,107)(94,105)(96,104)(97,111)(98,112)(101,114)(110,113);(54,55)(56,66)(57,71,73,62)(58,75)(59,81)(60,64)(61,68)(63,79)(65,78)(67,92,95,113)(69,93)(70,99)(72,102,77,110)(74,87,104,101)(76,91)(80,107)(82,88)(83,94,100,97)(84,109)(85,98)(86,105,89,111)(90,112)(96,115,106,117)(103,114,108,116)Polycyclic presentation:
2^8,53|a^2=f,d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,d^b=dg,e^b=eh,g^b=gh,i^b=i^52,d^c=dh,f^c=fh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85274);