Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C53×#3496 ⋊ C2 |
| Sylow | C53 ⋊ #25773 |
1770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 73 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)(54,56,57,55)(59,65)(63,66)(64,72)(71,73);(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)(59,64)(60,67,68,69)(62,70)(63,71,66,73)(65,72);(54,55,57,56)(58,60,62,68)(59,63,65,66)(61,69,70,67)(64,71,72,73);(55,56)(58,59)(60,66)(61,64)(62,65)(63,68)(67,71)(69,73)(70,72)Polycyclic presentation:
2^8,53|b^2=e,c^2=f,d^2=eh,b^a=be,c^a=cf,d^a=de,g^a=gh,c^b=cg,f^b=fh,g^c=gh,i^c=i^521187 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 224858);