Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1379 ⋊ C2 |
| Sylow | C53 ⋊ #12947 |
380 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 105 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)(55,64)(56,70)(58,77)(59,82)(60,78)(61,85)(62,79)(63,86)(65,75)(66,96)(67,92)(68,94)(69,98)(71,103)(72,108)(73,104)(74,106)(76,80)(81,113)(83,93)(84,105)(87,110)(88,101)(89,116)(90,115)(91,97)(95,111)(99,114)(100,117)(102,109)(107,112);(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)(54,56,60,73,62,74,61,84)(55,63,67,88,68,90,83,89)(57,70,78,104,79,106,85,105)(58,72,80,107,81,109,59,71)(64,86,92,101,94,115,93,116)(65,87,66,69,95,99,97,100)(75,110,96,98,111,114,91,117)(76,112,113,102,82,103,77,108);(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)(54,55,60,67,62,68,61,83)(56,69,73,99,74,100,84,87)(57,75,78,96,79,111,85,91)(58,66,80,95,81,97,59,65)(63,72,88,107,90,109,89,71)(64,76,92,113,94,82,93,77)(70,101,104,115,106,116,105,86)(98,108,114,112,117,102,110,103)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,i^a=i^52,d^b=dg,e^b=egh,g^b=gh,i^b=i^52,d^c=dgh,e^c=egh,g^c=gh,i^c=i^521502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 86247);