Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #18951 |
790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 101 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)(54,58,60,55)(56,65,66,61)(57,62,59,67)(63,64,69,68)(71,78)(76,91)(77,93)(79,86)(83,95)(90,101)(92,94)(96,100);(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)(54,57,60,59)(55,62,58,67)(56,64,66,68)(61,69,65,63)(70,73)(71,77)(72,80)(74,88)(75,84)(76,90)(78,93)(79,95)(81,99)(82,97)(83,86)(85,89)(87,98)(91,101)(92,100)(94,96);(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)(55,61)(57,64)(58,65)(59,68)(60,66)(62,69)(63,67)(70,72,75,82)(71,76,78,91)(73,80,84,97)(74,87,89,81)(77,90,93,101)(79,94,86,92)(83,100,95,96)(85,99,88,98);(54,55,60,58)(56,63,66,69)(57,62,59,67)(61,68,65,64)(70,71)(72,76)(73,83)(74,86)(75,78)(77,85)(79,89)(80,96)(81,94)(82,91)(84,95)(87,92)(88,93)(90,98)(97,100)(99,101)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,c^2=g,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eg,f^a=fh,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=eh,f^c=fh,i^c=i^52713 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 150356);