Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1814 ⋊ C2 |
| Sylow | C53 ⋊ #12747 |
886 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57)(55,63)(56,68)(58,73)(59,81)(60,74)(61,75)(62,84)(64,88)(65,90)(66,89)(67,93)(69,97)(70,100)(71,99)(72,82)(76,107)(77,104)(78,110)(79,105)(80,106)(83,98)(85,113)(86,102)(87,112)(91,96)(92,114)(94,116)(95,115)(101,117)(103,108)(109,111);(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)(55,62)(57,68)(58,77)(59,70)(60,83)(61,71)(63,84)(64,91)(65,85)(66,87)(67,76)(69,79)(72,102)(73,104)(74,98)(75,99)(78,101)(80,109)(81,100)(82,86)(88,96)(89,112)(90,113)(92,94)(93,107)(95,108)(97,105)(103,115)(106,111)(110,117)(114,116);(54,55)(56,67)(57,72,75,90)(58,76)(59,65)(60,82)(61,66)(62,69)(63,74,89,81)(64,79)(68,96,99,116)(70,94)(71,95)(73,88,106,114)(77,85)(78,92)(80,108)(83,91)(84,111,112,104)(86,109)(87,101)(93,98,115,100)(97,102,117,113)(103,110,107,105)Polycyclic presentation:
2^8,53|a^2=f,d^2=gh,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dg,g^b=gh,i^b=i^52,e^c=eh,f^c=fh878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85283);