Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #11458 |
364 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 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)(56,64)(60,70)(65,77)(66,78)(71,75)(72,81)(79,85)(82,84);(54,56)(55,60,61,70)(57,65)(58,66)(59,64)(62,75,73,71)(63,72,74,81)(67,77)(68,79)(69,78)(76,84,83,82)(80,85);(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)(54,55,57,62,58,63,68,76,59,61,67,73,69,74,80,83)(56,60,65,71,66,72,79,82,64,70,77,75,78,81,85,84)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,e^2=g,g^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^52,c^b=ch,d^b=dh,e^b=ef,e^d=eh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78762);