Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C53×#341 ⋊ C2 |
| Sylow | C53 ⋊ #11709 |
450 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 111 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 — 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)(62,65,68,67)(63,70,73,72)(64,75,78,77)(66,79,83,82)(69,84,86,85)(71,87,89,80)(74,90,91,88)(76,81,93,92);(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)(54,56)(55,58)(57,61)(59,60)(62,64)(63,69)(65,75)(66,81)(67,77)(68,78)(70,84)(71,88)(72,85)(73,86)(74,87)(76,82)(79,93)(80,91)(83,92)(89,90);(54,55)(56,60,61,58)(57,59)(62,63,65,70,68,73,67,72)(64,74,77,88,78,91,75,90)(66,80,79,71,83,87,82,89)(69,81,85,76,86,92,84,93)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,g^a=gh,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^b=i^521514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79820);