Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C53×#3028 ⋊ C2 |
| Sylow | C53 ⋊ #25800 |
1402 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)(54,58,76,87,60,78,59,77)(55,63,79,105,65,88,64,75)(56,68,80,106,70,98,69,97)(57,72,93,109,74,103,73,102)(61,82,91,112,83,96,66,90)(62,84,104,117,86,110,85,101)(67,94,100,116,71,99,95,114)(81,107,92,113,108,115,89,111);(54,57)(55,62)(56,67,70,71)(58,72)(59,73)(60,74)(61,81,83,108)(63,84)(64,85)(65,86)(66,89,91,92)(68,94,98,99)(69,95,80,100)(75,101)(76,93)(77,102)(78,103)(79,104)(82,107,96,115)(87,109)(88,110)(90,111,112,113)(97,114,106,116)(105,117);(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)(54,56,59,69,60,70,76,80)(55,61,64,66,65,83,79,91)(57,71,73,100,74,67,93,95)(58,68,77,97,78,98,87,106)(62,81,85,89,86,108,104,92)(63,82,75,90,88,96,105,112)(72,99,102,116,103,94,109,114)(84,107,101,111,110,115,117,113);(54,55,60,65)(56,66,70,91)(57,62,74,86)(58,75,78,105)(59,79,76,64)(61,80,83,69)(63,87,88,77)(67,92,71,89)(68,96,98,82)(72,101,103,117)(73,104,93,85)(81,95,108,100)(84,109,110,102)(90,106,112,97)(94,107,99,115)(111,114,113,116)Polycyclic presentation:
2^8,53|a^2=h,b^2=e,c^2=f,d^2=eh,e^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,g^a=gh,c^b=cg,f^b=fh,i^b=i^52,g^c=gh,i^d=i^52794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 225176);