Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #13329 |
578 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 117 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) = 6784 |
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)(59,61)(63,70)(65,82)(66,85)(67,83)(69,88)(71,86)(72,73)(74,80)(75,90)(76,81)(77,84)(78,87)(89,91)(92,93);(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)(60,61)(62,64,68,79)(63,69,74,90)(65,81,66,84)(67,87,83,78)(70,88,80,75)(71,91,72,92)(73,93,86,89)(76,85,77,82);(54,55)(56,57)(62,63,68,74)(64,75,79,88)(65,80,66,70)(67,86,83,73)(69,77,90,76)(71,85,72,82)(78,92,87,91)(81,93,84,89)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,d^2=gh,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,c^b=cf,d^b=dg,e^b=eg,g^b=gh,i^b=i^52,d^c=dg,e^c=eg,g^c=gh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88420);