Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C22×#117×C53 ⋊ C2 |
| Sylow | C53 ⋊ #34065 |
3134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 5 generators on 77 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)(62,65,66,73)(63,69,68,75)(64,72,71,77)(67,74,70,76);(63,68)(67,70)(69,75)(74,76);(59,61)(64,71)(67,70)(72,77)(74,76);(54,56,57,55)(62,64)(63,67)(65,72)(66,71)(68,70)(69,74)(73,77)(75,76);(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)(54,55,57,56)(58,59)(60,61)(62,63)(64,70)(65,69)(66,68)(67,71)(72,76)(73,75)(74,77)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,e^2=f,b^a=bf,c^a=cg,d^a=df,i^a=i^52,c^b=cf2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 328335);