Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1388 ⋊ C2 |
| Sylow | C53 ⋊ #12995 |
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 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)(55,64)(56,71)(58,83)(59,86)(60,87)(61,79)(62,81)(63,88)(65,97)(66,100)(67,101)(68,77)(69,95)(70,102)(72,109)(73,111)(74,112)(75,106)(76,108)(78,85)(80,84)(82,107)(89,113)(90,117)(91,115)(92,116)(93,99)(94,98)(96,104)(103,114)(105,110);(54,56,61,73,62,76,59,75)(55,63,68,89,69,92,66,91)(57,71,79,111,81,108,86,106)(58,82,60,72,85,74,84,110)(64,88,77,113,95,116,100,115)(65,96,67,70,99,90,98,103)(78,112,80,105,83,107,87,109)(93,117,94,114,97,104,101,102);(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)(54,55,60,67,61,68,85,99,62,69,84,98,59,66,58,65)(56,70,74,92,75,96,72,89,76,103,82,63,73,90,110,91)(57,77,80,97,79,95,83,101,81,100,87,93,86,64,78,94)(71,104,107,115,106,114,105,116,108,117,112,113,111,102,109,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,d^2=gh,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^52,d^b=dg,e^b=eh,f^b=fg,g^b=gh,d^c=dh,e^c=eh,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, 86527);