Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7472 |
166 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 6784 |
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)(58,60,63,76,64,77,81,91,62,75,84,108,85,109,83,107,66,79,87,111,89,113,82,106,65,78,86,110,80,105,61,74)(59,67,70,93,71,94,99,114,90,117,115,121,116,120,97,104,72,95,100,118,101,119,96,103,69,92,98,112,88,102,68,73);(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)(58,59,62,69,66,72,65,90)(60,73,75,103,79,104,78,114)(61,70,81,98,83,100,82,115)(63,68,84,96,87,97,86,99)(64,88,85,101,89,116,80,71)(67,91,92,107,95,106,117,74)(76,102,108,119,111,120,110,94)(77,112,109,118,113,121,105,93)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fg,d^2=h,e^2=f,f^2=gh,g^2=h,b^a=bc,c^a=cf,e^a=efg,f^a=fg,g^a=gh,i^a=i^523404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57271);