Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7253 |
328 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 95 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 — 2 generators on 93 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)(55,58,60,59)(62,64,66,75,67,73,78,87)(63,68,70,81,71,72,84,86)(65,74,76,88,77,79,89,90)(69,80,82,91,83,85,92,93);(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)(56,58)(57,60)(59,61)(62,63,65,69,67,71,77,83)(64,72,74,85,73,68,79,80)(66,70,76,82,78,84,89,92)(75,81,88,91,87,86,90,93)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=f,d^2=h,e^2=h,b^a=bc,c^a=cf,e^a=efg,i^a=i^52,c^b=cg,g^b=gh,i^b=i^52,e^c=eh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56698);