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 ⋊ #12889 |
310 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 310 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) = 97 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 97 points:
(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)(59,63)(62,65)(66,69,70,85,89,82,71,84,73,87,90,83,72,86,81,68)(67,75,76,94,92,97,77,74,79,80,91,96,78,93,88,95);(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)(58,60,61,64)(59,62,63,65)(66,68,81,86,72,83,90,87,73,84,71,82,89,85,70,69)(67,74,88,97,78,94,91,75,79,95,77,93,92,96,76,80);(54,55,56,57)(58,59)(60,62)(61,63)(64,65)(66,67)(68,80)(69,74)(70,88)(71,91)(72,92)(73,79)(75,84)(76,81)(77,90)(78,89)(82,94)(83,93)(85,97)(86,96)(87,95)Polycyclic presentation:
2^8,53|a^2=f,b^2=eh,c^2=d,d^2=gh,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,i^c=i^521220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85949);