Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #8521 |
690 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 107 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 101 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)(54,57,58,65)(55,60,61,67)(56,63,64,69)(59,66,62,68)(70,73)(71,77)(72,81)(74,85)(75,86)(76,89)(78,91)(79,84)(80,94)(82,96)(83,97)(87,100)(88,101)(90,98)(92,95)(93,99);(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)(54,56)(55,59)(57,63)(58,64)(60,66)(61,62)(65,69)(67,68)(70,72,75,83)(71,76,79,90)(73,81,86,97)(74,87,88,82)(77,89,84,98)(78,92,93,80)(85,100,101,96)(91,95,99,94);(54,55)(56,62,64,59)(57,60)(58,61)(63,68,69,66)(65,67)(70,71)(72,80,83,92)(73,84,86,77)(74,78)(75,79)(76,82,90,87)(81,95)(85,99,101,91)(88,93)(89,96)(94,97)(98,100)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=g,d^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,f^b=fgh,i^b=i^52,f^c=fh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62082);