Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1738 ⋊ C2 |
| Sylow | C53 ⋊ #28594 |
780 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)(55,59)(58,60)(64,74)(69,84)(73,90)(75,76)(78,92)(83,93)(85,91)(86,89);(62,65,66,79,68,80,67,82)(63,70,71,77,72,88,81,87)(64,73,75,78,74,90,76,92)(69,83,85,89,84,93,91,86);(54,56,57,61)(55,58,59,60)(62,64,67,76,68,74,66,75)(63,69,71,85,72,84,81,91)(65,78,79,90,80,92,82,73)(70,86,87,93,88,89,77,83);(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)(56,60)(57,59)(58,61)(62,63)(64,69)(65,77)(66,81)(67,71)(68,72)(70,79)(73,89)(74,84)(75,91)(76,85)(78,83)(80,87)(82,88)(86,90)(92,93)Polycyclic presentation:
2^8,53|b^2=eg,c^2=f,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^52,c^b=cg,d^b=dh,g^c=gh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 262592);