Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2161 ⋊ C2 |
| Sylow | C53 ⋊ #12942 |
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(54,57)(55,64)(56,70)(58,77)(59,76)(60,78)(61,85)(62,79)(63,86)(65,75)(66,92)(67,93)(68,95)(69,99)(71,107)(72,109)(73,104)(74,106)(80,102)(81,91)(82,113)(83,94)(84,105)(87,117)(88,115)(89,101)(90,116)(96,110)(97,112)(98,111)(100,114)(103,108);(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)(54,56,60,73,62,74,61,84)(55,63,67,88,68,90,83,89)(57,70,78,104,79,106,85,105)(58,80,81,108,82,72,59,71)(64,86,93,115,95,116,94,101)(65,96,66,69,97,87,98,100)(75,110,92,99,112,117,111,114)(76,107,77,102,91,103,113,109);(54,55,60,67,62,68,61,83)(56,69,73,87,74,100,84,96)(57,75,78,92,79,112,85,111)(58,66,81,97,82,98,59,65)(63,80,88,108,90,72,89,71)(64,91,93,113,95,76,94,77)(70,101,104,86,106,115,105,116)(99,109,117,107,114,102,110,103)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,d^2=gh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,d^b=dg,e^b=eg,g^b=gh,d^c=dg,e^c=egh,g^c=gh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86206);