Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C53 ⋊ #13583 |
416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 416 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) = 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)(54,57,59,70)(55,61,64,78)(56,66,68,81)(58,69,72,83)(60,73,75,85)(62,76,63,77)(65,79,74,84)(67,80,71,82);(54,56)(55,60)(57,66)(58,71)(59,68)(61,73)(62,74)(63,65)(64,75)(67,72)(69,82)(70,81)(76,84)(77,79)(78,85)(80,83);(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)(56,65,67,60)(57,61)(58,63,72,62)(59,64)(66,79,80,73)(68,74,71,75)(69,77,83,76)(70,78)(81,84,82,85)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,d^2=gh,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^52,d^b=dgh,e^b=efg,f^b=fh,e^d=egh,f^e=fh1178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 89880);