Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7544 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 2 generators on 117 points:
(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)(54,56,57,70,62,73,61,60)(55,63,64,69,68,67,74,89)(58,71,75,84,80,99,79,78)(59,72,76,97,83,100,82,81)(65,85,87,95,92,91,101,110)(66,86,88,96,94,93,102,111)(77,98,103,107,106,115,105,104)(90,108,109,114,113,112,116,117);(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)(54,55,58,65,59,66,77,90,60,67,78,91,81,93,104,112,61,64,79,87,82,88,105,109,73,89,99,110,100,111,115,117,62,68,80,92,83,94,106,113,70,63,84,85,97,86,107,108,57,74,75,101,76,102,103,116,56,69,71,95,72,96,98,114)Polycyclic presentation:
2^8,53|a^2=d,b^2=c,c^2=h,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,c^a=ch,i^b=i^522192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57465);