Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#16810342 |
| Sylow | C53 ⋊ C4⋊C64 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 2 generators on 121 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)(54,55,56,57);(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)(55,57)(58,59,60,65,61,66,70,80,62,67,71,81,74,84,90,100,63,68,72,82,75,85,91,101,77,87,93,103,96,106,110,115,64,69,73,83,76,86,92,102,78,88,94,104,97,107,111,116,79,89,95,105,98,108,112,117,99,109,113,118,114,119,120,121)Polycyclic presentation:
2^8,53|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,i^a=i^523488 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57464);