Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#1458 ⋊ C2 |
| Sylow | C53 ⋊ #11546 |
460 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 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)(54,56,58,64)(55,60,62,68)(57,63,65,69)(59,66,61,67)(70,72,74,78)(71,76,77,84)(73,79,81,85)(75,82,80,83);(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)(55,59)(60,66)(61,62)(67,68)(71,75)(72,78)(76,83)(77,80)(79,85)(82,84);(54,55,57,61,58,62,65,59)(56,60,63,67,64,68,69,66)(70,71)(72,76)(73,80,81,75)(74,77)(78,84)(79,83,85,82)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,e^2=g,b^a=bd,d^a=df,f^a=fh,c^b=cgh,e^b=ef,i^b=i^52,e^d=eh1181 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79107);