Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #12450 |
206 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 101 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)(70,72,73,81)(71,77,76,91)(74,87,84,101)(75,90,85,83)(78,94,92,100)(79,95,89,93)(80,97,96,86)(82,99,98,88);(54,56,63,67,58,65,57,64)(55,59,66,69,61,68,60,62)(71,76)(77,91)(78,92)(79,89)(80,96)(86,97)(93,95)(94,100);(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)(54,55,58,61)(56,62,65,69)(57,66,63,60)(59,67,68,64)(70,71)(72,80)(73,76)(74,86)(75,89)(77,82)(78,88)(79,85)(81,96)(83,100)(84,97)(87,95)(90,94)(91,98)(92,99)(93,101)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=h,d^2=f,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,i^a=i^52,e^c=eg,g^c=gh,i^c=i^521499 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83887);