Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1458 ⋊ C2 |
| Sylow | C53 ⋊ #18308 |
1188 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
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)(62,66,67,78)(63,70,71,77)(64,73,74,88)(65,75,76,90)(68,80,81,87)(69,82,83,89)(72,85,86,93)(79,91,84,92);(62,65)(63,69)(64,72)(66,75)(67,76)(68,79)(70,82)(71,83)(73,85)(74,86)(77,89)(78,90)(80,91)(81,84)(87,92)(88,93);(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)(56,61)(59,60)(62,64)(63,68)(65,72)(66,73)(67,74)(69,79)(70,80)(71,81)(75,85)(76,86)(77,87)(78,88)(82,91)(83,84)(89,92)(90,93);(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)(56,58)(57,60)(59,61)(62,63,67,71)(64,68,74,81)(65,69,76,83)(66,77,78,70)(72,84,86,79)(73,87,88,80)(75,89,90,82)(85,91,93,92)Polycyclic presentation:
2^8,53|a^2=h,d^2=h,e^2=g,b^a=be,c^a=cf,d^a=dh,e^a=eg,i^a=i^52,e^b=eg,f^b=fh,i^b=i^52,e^c=eh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 143609);