Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#451 ⋊ C2 |
| Sylow | C53 ⋊ #24400 |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(55,57);(58,61,64,77)(59,66,69,84)(60,70,72,86)(62,76,63,75)(65,79,81,88)(67,83,68,73)(71,87,78,74)(80,89,85,82);(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)(55,57)(58,60)(59,65)(61,74)(62,71)(63,78)(64,72)(66,82)(67,80)(68,85)(69,81)(70,76)(73,88)(75,86)(77,87)(79,83)(84,89);(54,55)(56,57)(58,59,62,67,64,69,63,68)(60,65,71,80,72,81,78,85)(61,73,75,84,77,83,76,66)(70,82,74,88,86,89,87,79)Polycyclic presentation:
2^8,53|a^2=f,c^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,g^b=gh,i^b=i^52,f^c=fh,g^c=gh1031 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 206853);