Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1425 ⋊ C2 |
| Sylow | C53 ⋊ #13702 |
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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)(54,56)(55,64)(57,70)(58,78)(59,71)(60,69)(61,72)(62,81)(63,88)(65,95)(66,93)(67,92)(68,94)(73,102)(74,100)(75,105)(76,99)(77,103)(79,106)(80,104)(82,107)(83,110)(84,108)(85,91)(86,109)(87,112)(89,101)(90,113)(96,116)(97,115)(98,114)(111,117);(54,55,63,87,59,66,76,85,58,65,89,97,79,96,57,62,61,68,73,84,80,98,75,83,60,67,90,111,74,82,77,86)(56,64,88,112,71,93,99,91,78,95,101,115,106,116,70,81,72,94,102,108,104,114,105,110,69,92,113,117,100,107,103,109);(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)(55,62)(56,69)(57,73)(58,60)(59,74)(63,77)(64,91)(65,85)(66,97)(67,83)(68,86)(70,101)(71,104)(72,78)(75,89)(76,90)(79,80)(81,92)(82,84)(87,96)(88,105)(93,112)(94,110)(95,109)(98,111)(99,102)(103,113)(107,115)(108,114)(116,117)Polycyclic presentation:
2^8,53|b^2=dfh,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fg,g^a=gh,i^a=i^52,e^c=eh,i^c=i^521034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90444);