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 ⋊ #13151 |
332 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 101 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:
(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)(55,57)(58,60,61,73,63,75,78,81,65,77,79,89,64,76,62,74)(59,67,68,86,80,85,87,88,71,84,82,83,70,66,69,72);(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)(58,60,61,73,63,75,78,81,65,77,79,89,64,76,62,74)(59,66,82,88,80,67,69,83,71,85,68,72,70,84,87,86);(54,55)(56,57)(58,59,63,70,65,71,64,80)(60,72,75,83,77,88,76,86)(61,69,78,82,79,87,62,68)(66,81,84,89,85,74,67,73)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfg,c^2=d,d^2=gh,e^2=g,f^2=h,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, 87509);