Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2049 ⋊ C2 |
| Sylow | C53 ⋊ #24296 |
1270 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)(54,58,60,80,61,81,59,79)(55,64,82,106,66,92,65,78)(56,69,83,107,71,99,70,98)(57,74,76,103,77,104,75,102)(62,85,86,111,87,97,67,93)(63,89,72,100,91,113,90,105)(68,94,73,101,96,115,95,114)(84,108,109,117,110,116,88,112);(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)(54,57)(55,63)(56,68)(58,74)(59,75)(60,76)(61,77)(62,84)(64,89)(65,90)(66,91)(67,88)(69,94)(70,95)(71,96)(72,82)(73,83)(78,105)(79,102)(80,103)(81,104)(85,108)(86,109)(87,110)(92,113)(93,112)(97,116)(98,114)(99,115)(100,106)(101,107)(111,117);(54,56,59,70,61,71,60,83)(55,62,65,67,66,87,82,86)(57,73,75,68,77,95,76,96)(58,69,79,98,81,99,80,107)(63,88,90,110,91,109,72,84)(64,85,78,93,92,97,106,111)(74,101,102,94,104,114,103,115)(89,112,105,116,113,117,100,108);(54,55)(56,67)(57,72)(58,78)(59,82)(60,65)(61,66)(62,70)(63,76)(64,79)(68,84)(69,97)(71,86)(73,88)(74,89)(75,91)(77,90)(80,92)(81,106)(83,87)(85,99)(93,98)(94,112)(95,109)(96,110)(100,102)(101,116)(103,105)(104,113)(107,111)(108,114)(115,117)Polycyclic presentation:
2^8,53|b^2=e,d^2=eh,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,g^b=gh,f^c=fh,g^c=gh,i^c=i^52,i^d=i^52638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 205604);