Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1420 ⋊ C2 |
| Sylow | C53 ⋊ #13625 |
290 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 79 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)(54,57,61,60)(55,63,66,84)(56,68,72,70)(58,73,79,78)(59,74,83,82)(62,86,89,87)(64,90,94,112)(65,80,96,93)(67,98,102,100)(69,85,107,105)(71,81,109,104)(75,110,97,115)(76,111,106,113)(77,91,103,114)(88,99,116,95)(92,108,101,117);(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)(55,62)(57,68)(58,76)(59,81)(60,70)(61,72)(63,86)(64,92)(65,95)(66,89)(67,97)(69,103)(71,82)(73,111)(74,109)(75,102)(77,107)(78,113)(79,106)(80,88)(83,104)(84,87)(85,114)(90,108)(91,105)(93,116)(94,101)(96,99)(98,115)(100,110)(112,117);(54,55,57,63,61,66,60,84)(56,67,70,100,72,102,68,98)(58,75,73,110,79,97,78,115)(59,80,74,96,83,93,82,65)(62,85,87,69,89,105,86,107)(64,91,90,103,94,114,112,77)(71,108,104,92,109,117,81,101)(76,95,113,116,106,99,111,88)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,d^2=fgh,e^2=h,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,d^b=dfh,e^b=eh,f^b=fg,g^b=gh,i^b=i^52,i^c=i^52728 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90043);