Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12676 |
306 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 147 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) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 points:
(1,2)(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)(54,56,57,55)(59,65)(64,77)(66,80)(67,81)(68,84)(78,79)(82,85)(83,89);(58,60,62,70,63,72,74,71)(59,64,67,78,65,77,81,79)(61,73,75,69,76,86,88,87)(66,82,83,68,80,85,89,84);(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)(54,55,57,56)(58,59,61,66,74,81,88,89,63,65,76,80,62,67,75,83)(60,68,69,78,70,85,86,77,72,84,87,79,71,82,73,64)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=deg,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ch,i^a=i^52,d^b=dg,e^b=eg,g^b=gh,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, 84986);