Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1384 ⋊ C2 |
| Sylow | C53 ⋊ #13075 |
458 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 458 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)(55,62)(56,68)(58,77)(59,75)(60,74)(61,83)(63,88)(64,72)(65,87)(66,90)(67,95)(69,99)(70,97)(71,98)(73,80)(76,106)(78,107)(79,109)(81,105)(82,108)(84,111)(85,104)(86,89)(91,113)(92,112)(93,110)(94,114)(96,101)(100,115)(102,117)(103,116);(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)(54,56,67,94,59,71,58,69,60,70,79,102,78,100,80,101)(55,61,82,103,65,84,63,66,64,85,76,92,81,91,89,93)(57,68,95,114,75,98,77,99,74,97,109,117,107,115,73,96)(62,83,108,116,87,111,88,90,72,104,106,112,105,113,86,110);(54,55)(56,66)(57,72,74,62)(58,76)(59,81)(60,64)(61,69)(63,79)(65,78)(67,89)(68,90,97,110)(70,93)(71,103)(73,106,77,108)(75,87,107,105)(80,82)(83,96,104,99)(84,94)(85,101)(86,95,88,109)(91,102)(92,100)(98,116,115,112)(111,117,113,114)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,e^b=eh,i^b=i^52,d^c=dh,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, 87021);