Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1381 ⋊ C2 |
| Sylow | C53 ⋊ #12559 |
554 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 199 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 — 3 generators on 89 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)(60,72)(65,79)(71,85)(73,87)(74,88)(75,89)(80,82)(81,86);(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)(54,55,56,57)(58,60,63,75,62,74,77,87,64,72,78,89,76,88,61,73)(59,65,68,81,69,82,84,85,70,79,83,86,67,80,66,71);(58,59,62,67,64,70,76,69)(60,71,74,86,72,85,88,81)(61,68,63,66,77,83,78,84)(65,75,80,87,79,89,82,73)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,d^2=gh,e^2=h,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fgh,g^a=gh,c^b=ch,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84456);