Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7546 |
66 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)(58,59,66,86,61,67,87,114,76,91,117,120,102,110,105,97,63,69,89,116,77,92,73,83,80,96,99,90,103,111,60,65,64,70,71,82,78,93,98,94,107,119,104,118,108,121,74,84,79,95,100,112,101,109,106,113,62,68,88,115,72,81,75,85);(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)(54,55,56,57)(59,65)(60,71)(61,72)(62,76)(63,79)(66,75)(67,90)(68,94)(69,97)(70,85)(73,104)(74,89)(77,108)(78,103)(80,107)(81,82)(83,91)(84,95)(86,111)(87,88)(92,120)(93,115)(96,114)(98,99)(100,105)(101,102)(106,117)(109,118)(110,116)(112,121)(113,119)Polycyclic presentation:
2^8,53|a^2=d,b^2=ceh,c^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^523398 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57470);