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 ⋊ #13207 |
486 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 167 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)(58,59,60,61)(63,69)(64,74)(70,85)(71,81)(75,90)(76,91)(77,82)(89,92);(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)(54,56,57,55)(62,64,73,89,67,76,65,75,66,74,80,92,78,91,79,90)(63,68,82,93,71,84,70,72,69,83,77,88,81,86,85,87);(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)(59,61)(62,63)(64,72)(65,77)(66,69)(67,81)(68,75)(70,80)(71,78)(73,85)(74,87)(76,93)(79,82)(83,90)(84,89)(86,92)(88,91)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,c^2=eh,d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^52,c^b=ch,i^b=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87805);