Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #12358 |
288 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 93 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)(54,56,58,55)(57,59,61,60);(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)(54,55,58,56)(57,60,61,59)(62,64,67,75)(63,68,71,85)(65,77,80,93)(66,82,78,74)(69,87,88,92)(70,89,81,84)(72,90,91,76)(73,86,83,79);(55,59)(56,60)(57,61)(62,63,67,71)(64,72,75,91)(65,76,80,90)(66,81,78,70)(68,83,85,73)(69,86,88,79)(74,92,82,87)(77,89,93,84)Polycyclic presentation:
2^8,53|a^2=h,b^2=gh,c^2=g,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,d^b=df,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=eg794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83284);