Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2179 ⋊ C2 |
| Sylow | C53 ⋊ #33465 |
642 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)(55,64)(57,72)(62,84)(65,90)(66,81)(67,93)(68,95)(73,99)(74,75)(76,106)(85,86)(91,94)(96,115)(97,105)(101,117)(102,103);(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)(54,57,59,74,61,72,60,75)(55,63,66,88,64,89,81,104)(56,68,70,97,71,95,82,105)(58,73,78,102,80,99,79,103)(62,83,85,108,84,110,86,109)(65,87,76,100,90,112,106,116)(67,92,94,113,93,114,91,111)(69,96,77,101,98,115,107,117);(54,56)(55,62)(57,68)(58,77)(59,70)(60,82)(61,71)(63,83)(64,84)(65,91)(66,85)(67,76)(69,79)(72,95)(73,101)(74,97)(75,105)(78,98)(80,107)(81,86)(87,111)(88,108)(89,110)(90,94)(92,100)(93,106)(96,103)(99,117)(102,115)(104,109)(112,113)(114,116);(54,55,59,66,61,64,60,81)(56,67,70,94,71,93,82,91)(57,63,74,88,72,89,75,104)(58,76,78,90,80,106,79,65)(62,77,85,98,84,107,86,69)(68,92,97,113,95,114,105,111)(73,100,102,112,99,116,103,87)(83,101,108,115,110,117,109,96)Polycyclic presentation:
2^8,53|a^2=f,c^2=f,e^2=gh,f^2=h,g^2=h,b^a=be,d^a=dh,e^a=eg,g^a=gh,e^b=eg,g^b=gh,d^c=dh,i^c=i^52,i^d=i^52896 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322992);