Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2138 ⋊ C2 |
| Sylow | C53 ⋊ #33587 |
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 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) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 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)(59,65)(64,77)(66,79)(67,80)(76,88)(78,83)(81,87)(82,89);(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)(58,60,63,70)(59,64,65,77)(61,72,74,86)(62,75,73,69)(66,82,79,89)(67,83,80,78)(68,84,85,71)(76,87,88,81);(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)(54,55,56,57)(58,59)(60,64)(61,66)(62,67)(63,65)(68,76)(69,78)(70,77)(71,81)(72,82)(73,80)(74,79)(75,83)(84,87)(85,88)(86,89);(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)(60,68)(61,71)(62,73)(64,76)(66,81)(67,80)(69,86)(70,85)(72,75)(74,84)(77,88)(78,89)(79,87)(82,83)Polycyclic presentation:
2^8,53|b^2=e,c^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^52,d^b=dh,i^b=i^52,f^c=fg,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323904);