Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #8520 |
976 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 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)(62,65)(63,69)(64,73)(66,77)(67,78)(68,81)(70,83)(71,76)(72,86)(74,88)(75,89)(79,92)(80,93)(82,90)(84,87)(85,91);(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)(54,56)(55,58)(57,61)(59,60)(62,64,67,75)(63,68,71,82)(65,73,78,89)(66,79,80,74)(69,81,76,90)(70,84,85,72)(77,92,93,88)(83,87,91,86);(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)(56,60,61,58)(57,59)(62,63)(64,72,75,84)(65,76,78,69)(66,70)(67,71)(68,74,82,79)(73,87)(77,91,93,83)(80,85)(81,88)(86,89)(90,92)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,d^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^52,d^b=dh,f^b=fgh,i^b=i^52,f^c=fh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62080);