Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#1746 ⋊ C2 |
| Sylow | C53 ⋊ #22282 |
810 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 211 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 — 4 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)(54,57,58,55)(56,60,61,59)(64,74)(69,83)(73,87)(75,76)(82,92)(84,90)(86,93)(88,89);(54,56,58,61)(55,59,57,60)(62,65,66,78,68,80,67,79)(63,70,71,77,72,85,81,91)(64,73,75,88,74,87,76,89)(69,82,84,86,83,92,90,93);(54,55,58,57)(56,60,61,59)(62,64,67,76,68,74,66,75)(63,69,71,84,72,83,81,90)(65,73,79,89,80,87,78,88)(70,82,77,86,85,92,91,93);(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)(59,60)(62,63,67,71,68,72,66,81)(64,69,76,84,74,83,75,90)(65,77,79,85,80,91,78,70)(73,86,89,92,87,93,88,82)Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,c^2=ef,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^52,c^b=ce,d^b=dh1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 183458);