Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×#101×C53 ⋊ C2 |
| Sylow | C53 ⋊ #21429 |
1010 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)(54,56,57,60)(55,59,58,61)(65,76)(69,82)(73,87)(77,86)(79,90)(83,92)(88,89)(91,93);(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)(59,61)(62,65,67,76)(63,69,70,82)(64,73,74,87)(66,77,72,86)(68,79,81,90)(71,83,84,92)(75,88,78,89)(80,91,85,93);(62,64,72,75,67,74,66,78)(63,68,71,85,70,81,84,80)(65,73,86,88,76,87,77,89)(69,79,83,93,82,90,92,91);(54,55)(56,59)(57,58)(60,61)(62,63,66,71,67,70,72,84)(64,68,75,80,74,81,78,85)(65,69,77,83,76,82,86,92)(73,79,88,91,87,90,89,93)Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,c^2=h,d^2=f,g^2=h,b^a=be,c^a=cf,e^a=eh,e^b=eh,g^b=gh,d^c=dh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 174974);