Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1379 ⋊ C2 |
| Sylow | C53 ⋊ #13339 |
534 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 121 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)(55,57)(58,61)(59,67)(60,73)(62,87)(63,83)(64,82)(65,84)(66,92)(68,102)(69,99)(70,98)(71,100)(72,105)(74,112)(75,110)(76,79)(77,111)(78,85)(80,88)(81,89)(86,109)(90,118)(91,117)(93,116)(94,96)(95,120)(97,103)(101,114)(104,115)(106,119)(107,121)(108,113);(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)(54,55)(56,57)(58,60,65,77)(59,66,71,95)(61,79,84,110)(62,86,90,113)(63,76,64,75)(67,96,100,116)(68,101,104,106)(69,94,70,93)(72,103,107,85)(73,83,111,82)(74,88,91,89)(78,114,97,119)(80,108,81,109)(87,117,118,112)(92,99,120,98)(102,121,115,105);(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)(58,59,65,71)(60,72,77,107)(61,78,84,97)(62,85,90,103)(63,70,64,69)(66,91,95,74)(67,80,100,81)(68,88,104,89)(73,92,111,120)(75,101,76,106)(79,116,110,96)(82,102,83,115)(86,93,113,94)(87,98,118,99)(105,108,121,109)(112,114,117,119)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,g^a=gh,i^a=i^52,c^b=cf,d^b=dg,e^b=eg,f^b=fh,g^b=gh,i^b=i^52,d^c=dgh,e^c=eg,f^c=fh,g^c=gh,i^c=i^521496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88489);