Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#2253 ⋊ C2 |
| Sylow | C53 ⋊ #33732 |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
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)(64,74)(69,81)(72,86)(75,83)(76,90)(84,87)(88,91)(89,93);(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)(62,64,73,89,67,76,77,83,65,74,85,93,78,90,66,75)(63,69,79,88,71,84,82,86,68,81,92,91,80,87,70,72);(54,56,57,61)(55,58,59,60)(63,68)(69,81)(70,82)(71,80)(72,86)(79,92)(84,87)(88,91);(54,55,57,59)(56,60,61,58)(62,63,65,68)(64,72,74,86)(66,79,77,92)(67,80,78,71)(69,83,81,75)(70,85,82,73)(76,91,90,88)(84,89,87,93)Polycyclic presentation:
2^8,53|a^2=e,b^2=eh,c^2=fg,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,d^c=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, 325094);