Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1416 ⋊ C2 |
| Sylow | C53 ⋊ #13690 |
204 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 55 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)(58,60,61,71)(59,66,65,87)(62,79,75,106)(63,84,76,109)(64,86,77,74)(67,92,88,118)(68,94,89,119)(69,95,85,91)(70,97,96,78)(72,101,99,81)(73,104,100,80)(82,116,107,113)(83,90,108,117)(93,121,110,103)(98,111,105,115)(102,114,112,120);(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)(59,65)(66,87)(67,88)(68,89)(69,85)(70,96)(78,97)(83,108)(90,117)(91,95)(92,118)(93,110)(94,119)(98,105)(103,121)(111,115);(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)(55,57)(58,59)(60,70)(61,65)(62,78)(63,83)(64,85)(66,72)(67,81)(68,80)(69,77)(71,96)(73,103)(74,105)(75,97)(76,108)(79,94)(82,115)(84,92)(86,98)(87,99)(88,101)(89,104)(90,113)(91,112)(93,120)(95,102)(100,121)(106,119)(107,111)(109,118)(110,114)(116,117)Polycyclic presentation:
2^8,53|b^2=dh,c^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^52,i^b=i^52,e^c=ef,f^c=fg,g^c=gh,i^c=i^521037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90378);