Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C53×#362 ⋊ C2 |
| Sylow | C53 ⋊ #13069 |
450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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)(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)(54,57)(55,63)(56,69)(58,78)(59,82)(60,75)(61,76)(62,85)(64,92)(65,91)(66,90)(67,94)(68,99)(70,105)(71,104)(72,103)(73,83)(74,80)(77,109)(79,110)(81,102)(84,111)(86,108)(87,114)(88,115)(89,93)(95,116)(96,100)(97,113)(98,112)(101,107)(106,117);(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)(54,56,68,98,60,71,58,70,61,72,79,106,59,81,80,107)(55,62,84,95,65,87,64,67,66,88,77,96,83,86,93,97)(57,69,99,112,75,104,78,105,76,103,110,117,82,102,74,101)(63,85,111,116,91,114,92,94,90,115,109,100,73,108,89,113);(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)(56,67)(57,73,76,91)(58,77)(59,65)(60,83)(61,66)(62,70)(63,75,90,82)(64,79)(68,93)(69,100,103,116)(71,95)(72,97)(74,89,78,92)(80,84)(81,96)(85,112,115,117)(86,106)(87,98)(88,107)(94,102,113,104)(99,109,110,111)(101,108,105,114)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,d^2=gh,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,e^b=eh,i^b=i^52,d^c=dh,e^c=eh,f^c=fh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86985);