Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7470 |
178 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)(59,66)(61,77)(62,80)(63,75)(64,73)(65,76)(67,90)(68,93)(69,88)(70,72)(71,89)(74,83)(78,101)(79,105)(81,108)(82,86)(84,102)(85,104)(87,96)(91,99)(92,114)(94,116)(95,107)(97,100)(98,113)(103,110)(106,120)(109,111)(112,118)(115,119)(117,121);(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)(58,59,62,68,63,69,81,94,64,70,82,95,84,97,109,117,65,71,83,96,85,98,110,118,61,67,78,91,79,92,106,115)(60,72,74,99,75,100,103,119,73,89,101,93,102,113,120,116,76,90,80,107,104,114,108,121,77,66,86,87,105,88,111,112)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=h,d^2=f,f^2=g,g^2=h,b^a=bc,i^a=i^52,c^b=ch,d^b=dh2192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57266);