Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C53×#367 ⋊ C2 |
| Sylow | C53 ⋊ #33460 |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
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)(58,62,64,60)(59,68,70,74)(61,71,65,75)(63,76,79,72)(66,83,84,77)(67,86,81,87)(69,82,88,85)(73,78,80,89);(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)(54,56,57,55)(58,61,64,65)(59,67,70,81)(60,71,62,75)(63,73,79,80)(66,82,84,85)(68,87,74,86)(69,77,88,83)(72,78,76,89);(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)(58,60,64,62)(59,66,70,84)(61,71,65,75)(63,78,79,89)(67,82,81,85)(68,83,74,77)(69,86,88,87)(72,73,76,80);(54,55,57,56)(58,59,64,70)(60,68,62,74)(61,67,65,81)(63,77,79,83)(66,76,84,72)(69,73,88,80)(71,87,75,86)(78,82,89,85)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=f,d^2=h,e^2=gh,g^2=h,b^a=be,d^a=dh,e^a=eg,g^a=gh,e^b=eg,g^b=gh,i^b=i^52,d^c=dh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322961);