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×#359 ⋊ C2 |
| Sylow | C53 ⋊ #13071 |
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 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)(58,79)(59,83)(60,75)(61,76)(62,85)(64,93)(65,91)(66,90)(67,95)(68,99)(70,105)(71,103)(72,104)(73,84)(74,81)(77,108)(78,101)(80,109)(82,102)(86,107)(87,114)(88,113)(89,94)(92,112)(96,116)(97,100)(98,111)(106,117)(110,115);(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)(54,56,68,98,59,82,58,78,61,72,80,106,60,71,81,70)(55,62,77,96,84,86,64,92,66,87,110,97,65,88,94,67)(57,69,99,111,83,102,79,101,76,104,109,117,75,103,74,105)(63,85,108,116,73,107,93,112,90,114,115,100,91,113,89,95);(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)(56,67,72,92)(57,73,76,91)(58,77)(59,65)(60,84)(61,66)(62,70,87,78)(63,75,90,83)(64,68)(69,100)(71,96,82,97)(74,89,79,93)(80,94)(81,110)(85,111)(86,106,88,98)(95,103)(99,115,109,108)(101,113)(102,112)(104,116)(105,107)(114,117)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,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=fh,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86999);