Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #19402 |
622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 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)(64,73)(68,82)(72,87)(74,89)(81,92)(83,90)(86,93)(88,91);(62,65,67,77)(63,69,71,84)(64,72,73,87)(66,79,80,76)(68,81,82,92)(70,85,78,75)(74,91,89,88)(83,93,90,86);(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)(54,55,56,58,57,59,60,61)(62,64)(63,68)(65,72)(66,74)(67,73)(69,81)(70,83)(71,82)(75,86)(76,88)(77,87)(78,90)(79,91)(80,89)(84,92)(85,93);(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)(55,58)(56,60)(59,61)(62,63,67,71)(64,68,73,82)(65,75,77,85)(66,78,80,70)(69,79,84,76)(72,86,87,93)(74,90,89,83)(81,91,92,88)Polycyclic presentation:
2^8,53|a^2=h,b^2=e,c^2=h,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^52,d^b=dh,i^b=i^52,f^c=fh881 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 154904);