Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7386 |
124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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) = 13568 |
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)(62,63,67,69)(64,73,76,84)(65,78,80,82)(66,81,79,71)(68,72,83,91)(70,74,86,77)(75,87,89,92)(85,93,88,90);(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)(54,55,56,58,57,59,60,61)(63,68,69,83)(64,72)(65,77)(66,79)(70,87,86,92)(71,88,81,85)(73,78,84,82)(74,80)(75,93)(76,91)(89,90)Polycyclic presentation:
2^8,53|a^2=d,b^2=h,c^2=egh,d^2=f,e^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^52,c^b=ceh,d^b=dh,e^b=eg,g^b=gh,i^b=i^522132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57028);