Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C53×B(4,𝔽2) ⋊ C2 |
| Sylow | C53 ⋊ #32899 |
3866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 3866 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 73 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)(58,61,62,68)(59,64,65,71)(60,66,67,72)(63,70,69,73);(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)(59,63)(61,66)(62,67)(64,70)(65,69)(68,72)(71,73);(58,59)(60,63)(61,64)(62,65)(66,70)(67,69)(68,71)(72,73);(54,55)(56,57)(63,69)(70,73)Polycyclic presentation:
2^8,53|d^2=h,b^a=be,c^a=cf,d^a=dg,f^b=fh,e^c=eh,i^d=i^52881 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 318342);