Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1415 ⋊ C2 |
| Sylow | C53 ⋊ #13615 |
298 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 121 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)(58,61,64,79)(59,66,70,69)(60,72,76,75)(62,77,83,110)(63,78,86,111)(65,87,89,97)(67,90,94,93)(68,91,96,84)(71,98,99,106)(73,100,103,102)(74,101,105,85)(80,107,113,112)(81,108,115,114)(82,109,116,119)(88,95,117,121)(92,104,118,120);(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)(58,60)(59,65)(61,72)(62,81)(63,85)(64,76)(66,87)(67,92)(68,95)(69,97)(70,89)(71,80)(73,82)(74,78)(75,79)(77,108)(83,115)(84,88)(86,101)(90,104)(91,117)(93,120)(94,118)(96,121)(98,107)(99,113)(100,109)(102,119)(103,116)(105,111)(106,112)(110,114);(54,55,56,57)(58,59)(60,71)(61,66)(62,80)(63,84)(64,70)(65,73)(67,82)(68,78)(69,79)(72,98)(74,104)(75,106)(76,99)(77,107)(81,95)(83,113)(85,92)(86,91)(87,100)(88,114)(89,103)(90,109)(93,119)(94,116)(96,111)(97,102)(101,118)(105,120)(108,117)(110,112)(115,121)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,d^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,d^b=df,f^b=fg,g^b=gh,i^c=i^521064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89999);