Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #7353 |
204 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 43 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 — 2 generators on 93 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)(62,64,67,75)(63,68,71,84)(65,73,77,91)(66,80,81,74)(69,85,86,72)(70,82,79,83)(76,88,92,87)(78,89,93,90);(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)(54,55,56,58,57,59,60,61)(62,63)(64,72,74,87)(65,76,77,92)(66,79,81,70)(67,71)(68,73,82,89)(69,78)(75,85,80,88)(83,90,84,91)(86,93)Polycyclic presentation:
2^8,53|a^2=d,b^2=h,c^2=g,d^2=f,e^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,c^b=cg,d^b=degh,e^b=eh,i^b=i^52,d^c=dgh,e^d=eh704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56948);