Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×#107×C53 ⋊ C2 |
| Sylow | C53 ⋊ #22614 |
778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
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)(66,70,69,75,72,74,71,67)(68,73,79,81,78,80,77,76);(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)(59,63)(62,65)(66,69,72,71)(67,70,75,74)(68,77,78,79)(73,76,80,81);(58,60,61,64)(59,62,63,65)(66,68,72,78)(67,73,75,80)(69,77,71,79)(70,76,74,81);(54,55,56,57)(58,59)(60,62)(61,63)(64,65)(66,67,71,74,72,75,69,70)(68,76,77,80,78,81,79,73)Polycyclic presentation:
2^8,53|a^2=g,b^2=fh,c^2=h,d^2=eh,e^2=h,g^2=h,b^a=be,c^a=cf,d^b=de,e^b=eh,g^b=gh,i^c=i^521526 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 187232);