Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C53×#1966 ⋊ C2 |
| Sylow | C53 ⋊ #29820 |
780 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 163 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 — 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)(54,56,57,60)(55,59,58,61);(56,60)(59,61)(62,65,68,81)(63,70,73,88)(64,74,76,90)(66,80,67,79)(69,83,85,92)(71,87,72,77)(75,91,82,78)(84,93,89,86);(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)(55,58)(59,61)(62,64)(63,69)(65,78)(66,75)(67,82)(68,76)(70,86)(71,84)(72,89)(73,85)(74,80)(77,92)(79,90)(81,91)(83,87)(88,93);(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)(54,55)(56,59)(57,58)(60,61)(62,63,66,71,68,73,67,72)(64,69,75,84,76,85,82,89)(65,77,79,88,81,87,80,70)(74,86,78,92,90,93,91,83)Polycyclic presentation:
2^8,53|a^2=f,c^2=h,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,i^a=i^52,c^b=cg,g^b=gh,i^b=i^52,d^c=de,f^c=fh,g^c=gh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 277020);