Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#2240 ⋊ C2 |
| Sylow | C53 ⋊ #33702 |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(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)(63,71)(69,82)(70,84)(72,87)(73,83)(81,91)(85,93)(86,92);(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)(55,59)(58,61)(62,64,65,75,78,90,80,89,68,77,79,88,67,76,66,74)(63,70,69,81,83,92,87,93,71,84,82,91,73,86,72,85);(54,56,57,60)(55,58,59,61)(62,63,66,72,67,73,79,82,68,71,80,87,78,83,65,69)(64,70,74,85,76,86,88,91,77,84,89,93,90,92,75,81);(54,55)(56,58)(57,59)(60,61)(63,69)(64,74)(65,66)(67,78)(71,82)(72,83)(73,87)(75,76)(77,89)(79,80)(81,85)(86,92)(88,90)(91,93)Polycyclic presentation:
2^8,53|b^2=f,c^2=e,e^2=gh,f^2=g,g^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fgh,g^a=gh,d^b=dh,i^d=i^521040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324895);