Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#1358 ⋊ C2 |
| Sylow | C53 ⋊ #12466 |
186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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)(56,72)(58,80)(59,85)(60,81)(61,86)(62,82)(63,89)(65,78)(66,99)(67,95)(68,100)(69,96)(70,101)(71,103)(73,108)(74,109)(75,106)(76,110)(77,107)(79,83)(84,112)(87,105)(88,111)(90,115)(91,104)(92,116)(93,114)(94,97)(98,117)(102,113);(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)(54,56,71,74,60,75,58,73,62,77,59,84,61,76,83,87)(55,63,88,90,67,91,65,70,69,93,66,98,68,92,97,102)(57,72,103,109,81,106,80,108,82,107,85,112,86,110,79,105)(64,89,111,115,95,104,78,101,96,114,99,117,100,116,94,113);(54,55,62,69)(56,70,77,102)(57,78,82,94)(58,66,83,88)(59,65,71,97)(60,68,61,67)(63,87,93,73)(64,79,96,80)(72,104,107,116)(74,91,84,92)(75,90,76,98)(81,111,86,99)(85,100,103,95)(89,110,114,106)(101,108,113,105)(109,115,112,117)Polycyclic presentation:
2^8,53|a^2=h,b^2=dg,d^2=fh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,g^a=gh,e^b=eh,i^b=i^52,d^c=dh,e^c=eg,g^c=gh,i^c=i^52629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83977);