Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #9022 |
572 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 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)(58,61)(59,64)(60,66)(62,69)(63,70)(65,68)(67,72)(71,73)(74,77,79,78)(75,81,83,82)(76,85,87,86)(80,88,89,84);(54,56,57,55)(58,60,62,67)(59,63,65,71)(61,66,69,72)(64,70,68,73)(74,76)(75,80)(77,85)(78,86)(79,87)(81,88)(82,84)(83,89);(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)(54,55,57,56)(58,59)(60,63)(61,68,69,64)(62,65)(66,70,72,73)(67,71)(74,75,78,82,79,83,77,81)(76,84,85,80,87,88,86,89)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eh,i^a=i^52,d^b=dg,e^b=eh,f^b=fg,d^c=dh,f^c=fh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 64602);