Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#1378 ⋊ C2 |
| Sylow | C53 ⋊ #13123 |
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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)(54,57,58,75,61,76,60,78)(55,63,64,88,66,74,79,104)(56,69,70,97,73,98,72,100)(59,77,68,95,81,87,80,106)(62,84,67,91,86,103,93,96)(65,89,83,108,90,105,94,115)(71,99,82,107,102,112,101,109)(85,110,92,113,111,117,114,116);(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)(54,56,68,82,58,70,81,102,61,73,80,101,60,72,59,71)(55,62,83,92,79,93,65,85,66,86,94,114,64,67,90,111)(57,69,95,107,75,97,87,112,76,98,106,109,78,100,77,99)(63,84,108,113,104,96,89,110,74,103,115,116,88,91,105,117);(54,55,59,65,60,64,80,83,61,66,81,90,58,79,68,94)(56,67,71,92,72,86,101,111,73,93,102,114,70,62,82,85)(57,74,77,105,78,104,106,115,76,63,87,89,75,88,95,108)(69,96,99,116,100,84,109,110,98,91,112,113,97,103,107,117)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=d,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^b=i^52,e^c=eh1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87314);