Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13281 |
366 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 163 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:
(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)(58,60,61,65)(59,62,63,64)(66,69,71,83,72,84,86,70)(67,74,76,75,77,85,87,91)(68,79,81,95,82,96,97,80)(73,88,89,78,90,93,92,94);(54,56,57,55)(66,68,69,79,71,81,83,95,72,82,84,96,86,97,70,80)(67,73,85,93,76,89,91,94,77,90,74,88,87,92,75,78);(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)(58,59,61,63)(60,64,65,62)(66,67)(68,78)(69,75)(70,85)(71,87)(72,77)(73,80)(74,83)(76,86)(79,92)(81,88)(82,94)(84,91)(89,96)(90,95)(93,97)Polycyclic presentation:
2^8,53|a^2=f,b^2=def,c^2=e,d^2=gh,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,i^a=i^523404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88165);