Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #12987 |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 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)(54,57)(55,63)(56,68)(58,77)(59,80)(60,74)(61,73)(62,84)(64,90)(65,92)(66,95)(67,72)(69,101)(70,100)(71,103)(75,82)(76,98)(78,106)(79,99)(81,88)(83,89)(85,104)(86,113)(87,110)(91,97)(93,105)(94,111)(96,108)(102,116)(107,109)(112,115)(114,117);(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)(54,56,59,79,60,70,81,107,61,69,82,71,58,76,78,102)(55,62,83,86,67,85,93,112,64,87,66,94,65,91,96,114)(57,68,80,99,74,100,88,109,73,101,75,103,77,98,106,116)(63,84,89,113,72,104,105,115,90,110,95,111,92,97,108,117);(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)(54,55,59,66,60,67,81,96,61,64,82,83,58,65,78,93)(56,62,71,86,70,85,102,112,69,87,79,94,76,91,107,114)(57,72,75,105,74,90,106,95,73,92,80,108,77,63,88,89)(68,97,99,115,100,84,109,111,101,104,103,117,98,110,116,113)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^52,d^b=dh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh,e^c=eh,f^c=fh1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86486);