Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #21751 |
1294 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1294 conjugacy classes of subgroups — too many to draw. Only its 235 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) = 3392 |
A minimal faithful permutation representation — 4 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)(55,59)(58,60)(62,66,67,79)(63,70,71,85)(64,73,74,78)(65,76,77,91)(68,81,82,84)(69,83,75,89)(72,87,88,90)(80,92,86,93);(56,61)(58,60)(62,65)(63,69)(64,72)(66,76)(67,77)(68,80)(70,83)(71,75)(73,87)(74,88)(78,90)(79,91)(81,92)(82,86)(84,93)(85,89);(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)(54,56)(55,58)(57,61)(59,60)(62,64,67,74)(63,68,71,82)(65,72,77,88)(66,78,79,73)(69,80,75,86)(70,84,85,81)(76,90,91,87)(83,93,89,92);(54,55)(56,60)(57,59)(58,61)(62,63)(64,68)(65,75,77,69)(66,70)(67,71)(72,86,88,80)(73,81)(74,82)(76,89,91,83)(78,84)(79,85)(87,93,90,92)Polycyclic presentation:
2^8,53|a^2=g,b^2=h,d^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=ce,d^b=dh,i^b=i^52,g^c=gh878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 178533);