Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #21250 |
1434 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)(61,73)(66,82)(69,84)(72,86)(74,75)(78,88)(83,89)(85,87);(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)(58,61,62,74,64,73,63,75)(59,66,68,72,67,82,76,86)(60,69,71,85,70,84,77,87)(65,78,79,83,81,88,80,89);(54,56,57,55)(58,60,62,71,64,70,63,77)(59,65,68,79,67,81,76,80)(61,69,74,85,73,84,75,87)(66,78,72,83,82,88,86,89);(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)(54,55,57,56)(58,59,63,68,64,67,62,76)(60,65,71,80,70,81,77,79)(61,72,75,82,73,86,74,66)(69,83,85,78,84,89,87,88)Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,c^2=f,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^52,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, 173593);