Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#1426 ⋊ C2 |
| Sylow | C53 ⋊ #13709 |
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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)(58,73)(59,81)(60,85)(61,76)(62,86)(64,89)(65,95)(66,97)(67,92)(69,100)(70,104)(71,102)(72,106)(74,94)(75,79)(77,91)(78,113)(80,111)(82,88)(83,101)(84,90)(87,107)(93,99)(96,109)(98,108)(103,117)(105,112)(110,115)(114,116);(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)(54,56,58,69,61,71,79,60)(55,62,64,66,67,84,77,98)(57,68,73,100,76,102,75,85)(59,70,78,94,83,105,114,82)(63,86,89,97,92,90,91,108)(65,87,93,80,96,115,103,106)(72,95,107,99,111,109,110,117)(74,101,112,116,88,81,104,113);(54,55,61,67)(56,66,71,98)(57,72)(58,77,79,64)(59,80,83,106)(60,84,69,62)(63,88)(65,94,96,82)(68,99)(70,103,105,93)(73,110)(74,92)(75,107)(76,111)(78,87,114,115)(81,97)(85,109)(86,113)(89,112)(90,116)(91,104)(95,100)(101,108)(102,117)Polycyclic presentation:
2^8,53|a^2=dg,b^2=d,d^2=h,e^2=fgh,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=ef,f^a=fg,g^a=gh,i^b=i^52,e^c=efh,f^c=fg,g^c=gh,i^c=i^52713 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90483);