Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #33315 |
806 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 331 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 generators on 81 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)(54,55,56,57)(68,75)(72,79)(74,81)(76,80);(66,68,70,76,69,75,77,80)(67,72,73,74,71,79,78,81);(58,60,61,65)(59,62,63,64)(67,71)(72,79)(73,78)(74,81);(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)(58,59,61,63)(60,64,65,62)(66,67,69,71)(68,74,75,81)(70,78,77,73)(72,80,79,76)Polycyclic presentation:
2^8,53|a^2=e,b^2=eh,c^2=f,d^2=g,f^2=h,b^a=be,c^a=cf,d^a=dg,f^a=fh,i^a=i^52,d^c=dh2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322159);