Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#2110 ⋊ C2 |
| Sylow | C53 ⋊ #13199 |
406 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 115 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:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,57)(55,63)(56,70,72,102)(58,79)(59,76)(60,75)(61,77)(62,85,86,111)(64,93)(65,90)(66,89)(67,91)(68,88,92,100)(69,99)(71,74,78,101)(73,103,80,109)(81,104)(82,107)(83,106,98,105)(84,110)(87,112,94,117)(95,113)(96,116)(97,114,108,115);(54,56,69,98,58,78,82,73,61,72,81,83,60,71,59,80)(55,62,84,97,64,92,96,87,67,86,95,108,66,68,65,94)(57,74,104,103,79,70,76,106,77,101,99,109,75,102,107,105)(63,88,113,112,93,85,90,115,91,100,110,117,89,111,116,114);(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)(54,55,59,65,60,66,81,95,61,67,82,96,58,64,69,84)(56,68,73,97,71,86,98,94,72,92,80,108,78,62,83,87)(57,63,76,90,75,89,104,113,77,91,107,116,79,93,99,110)(70,100,103,115,74,85,105,112,102,88,109,114,101,111,106,117)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=e,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^52,c^b=cg,d^b=dh,e^b=eh,f^b=fh,d^c=dh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87767);