Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#1420 ⋊ C2 |
| Sylow | C53 ⋊ #13718 |
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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:
(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)(54,56,59,82,60,67,79,70)(55,61,64,94,65,84,81,86)(57,73,76,112,72,101,108,110)(58,78,74,69,80,114,91,99)(62,89,90,103,88,97,106,117)(63,92,77,85,93,109,113,116)(66,96,104,71,95,107,98,105)(68,100,115,75,83,111,102,87);(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)(57,72)(62,88)(66,95)(68,83)(71,105)(73,101)(75,87)(76,108)(89,97)(90,106)(96,107)(98,104)(100,111)(102,115)(103,117)(110,112);(54,55,60,65)(56,66,67,95)(57,71,72,105)(58,77,80,113)(59,81,79,64)(61,83,84,68)(62,87,88,75)(63,91,93,74)(69,103,99,117)(70,104,82,98)(73,109,101,92)(76,96,108,107)(78,97,114,89)(85,110,116,112)(86,102,94,115)(90,111,106,100)Polycyclic presentation:
2^8,53|a^2=h,c^2=dg,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,e^b=eh,i^b=i^52,d^c=dh,e^c=efh,f^c=fg,g^c=gh707 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90531);