Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2151 ⋊ C2 |
| Sylow | C53 ⋊ #33634 |
534 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)(62,64,67,73)(63,69,72,83)(65,74,78,87)(66,75,77,88)(68,80,82,91)(70,84,81,92)(71,85,79,90)(76,89,86,93);(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)(63,68)(65,76)(66,77)(69,80)(70,71)(72,82)(74,89)(75,88)(78,86)(79,81)(83,91)(84,85)(87,93)(90,92);(54,56,57,61)(55,58,59,60)(64,73)(69,83)(74,87)(75,88)(80,91)(84,92)(85,90)(89,93);(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)(54,55,57,59)(56,60,61,58)(62,63,67,72)(64,69,73,83)(65,68,78,82)(66,79,77,71)(70,86,81,76)(74,80,87,91)(75,90,88,85)(84,93,92,89)Polycyclic presentation:
2^8,53|a^2=eh,b^2=e,d^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^52,d^b=dh,f^c=fg,g^c=gh,i^c=i^521502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324290);