Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2009 ⋊ C2 |
| Sylow | C53 ⋊ #25448 |
860 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 117 points:
(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)(54,58,61,83,60,81,59,80)(55,64,66,91,67,92,65,79)(56,70,82,109,72,101,71,100)(57,75,77,107,78,108,76,106)(62,85,86,111,87,99,68,95)(63,89,93,113,90,105,73,103)(69,96,98,117,74,104,97,116)(84,110,102,115,88,112,94,114);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57)(55,63)(56,69)(58,75)(59,76)(60,78)(61,77)(62,84)(64,89)(65,73)(66,93)(67,90)(68,94)(70,96)(71,97)(72,74)(79,103)(80,106)(81,108)(82,98)(83,107)(85,110)(86,102)(87,88)(91,113)(92,105)(95,114)(99,112)(100,116)(101,104)(109,117)(111,115);(54,56,60,72)(55,62)(57,74)(58,70,81,101)(59,71,61,82)(63,88,90,84)(64,85)(65,68)(66,86)(67,87)(69,78)(73,102,93,94)(75,104)(76,98)(77,97)(79,95)(80,100,83,109)(89,112,105,110)(91,111)(92,99)(96,108)(103,115,113,114)(106,117)(107,116);(54,55,61,65,60,67,59,66)(56,68,82,87,72,86,71,62)(57,73,76,63,78,93,77,90)(58,79,83,92,81,91,80,64)(69,88,97,94,74,84,98,102)(70,99,109,111,101,85,100,95)(75,105,106,103,108,89,107,113)(96,115,116,112,104,114,117,110)Polycyclic presentation:
2^8,53|a^2=fh,b^2=ef,d^2=eh,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,g^b=gh,f^c=fh,i^d=i^52638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 221126);