Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1388 ⋊ C2 |
| Sylow | C53 ⋊ #12830 |
378 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 103 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)(56,68)(58,78)(59,75)(60,84)(61,73)(62,85)(64,91)(65,94)(66,89)(67,95)(69,102)(70,99)(71,97)(72,76)(74,80)(77,110)(79,106)(81,112)(82,100)(83,90)(86,115)(87,114)(88,116)(92,104)(93,117)(96,101)(98,103)(105,108)(107,111)(109,113);(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)(54,56,60,70,61,71,59,82)(55,62,83,87,64,67,66,88)(57,68,84,99,73,97,75,100)(58,77,80,111,81,69,79,103)(63,85,90,114,91,95,89,116)(65,93,108,109,92,86,76,101)(72,96,94,117,105,113,104,115)(74,107,112,102,106,98,78,110);(54,55,59,66,61,64,60,83)(56,67,70,88,71,62,82,87)(57,72,75,104,73,105,84,94)(58,76,79,92,81,108,80,65)(63,78,89,106,91,112,90,74)(68,96,99,117,97,113,100,115)(69,101,103,93,77,109,111,86)(85,102,114,98,95,110,116,107)Polycyclic presentation:
2^8,53|a^2=f,b^2=dg,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,e^b=eh,f^b=fh,i^b=i^52,d^c=dh,e^c=eg,g^c=gh,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85711);