Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #21127 |
814 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 generators on 81 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)(58,60,61,64)(59,63,62,65)(66,70,71,69)(67,75,76,79)(68,78,72,80)(73,81,77,74);(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)(66,69,71,70)(67,74,76,81)(68,78,72,80)(73,79,77,75);(54,56,57,55)(59,62)(63,65)(66,68,71,72)(67,73,76,77)(69,78,70,80)(74,79,81,75);(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)(60,63)(61,62)(64,65)(66,67,71,76)(68,77,72,73)(69,79,70,75)(74,80,81,78)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,c^2=h,d^2=e,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^52,d^b=dh,f^c=fh,i^c=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 172676);