Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#2141 ⋊ C2 |
| Sylow | C53 ⋊ #13216 |
434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 101 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:
(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)(54,57)(55,63,66,91)(56,69,72,101)(58,75)(59,76)(60,78)(61,77)(62,85)(64,90,92,111)(65,73,83,106)(67,93)(68,98)(70,100,103,117)(71,74,82,110)(79,105,84,113)(80,108)(81,112)(86,114)(87,89)(88,104)(94,99)(95,115)(96,107)(97,116,102,109);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56,68,97,60,71,58,70,61,72,80,102,59,82,81,103)(55,62,84,94,65,87,64,67,66,88,79,95,83,86,92,96)(57,74,108,117,78,101,112,116,77,110,98,100,76,69,75,109)(63,89,105,107,73,104,111,99,91,114,113,93,106,85,90,115);(54,55)(56,67)(57,73,77,106)(58,79)(59,65)(60,83)(61,66)(62,70)(63,76,91,78)(64,80)(68,92)(69,99,101,115)(71,94)(72,96)(74,107,110,93)(75,111,112,90)(81,84)(82,95)(85,109,104,116)(86,102)(87,97)(88,103)(89,100,114,117)(98,113,108,105)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,c^2=eg,d^2=gh,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,c^b=cg,e^b=eh,f^c=fh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87842);