Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #8529 |
648 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 131 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)(54,56)(55,61)(57,63)(58,66)(59,64)(60,67)(62,69)(65,68)(70,73)(71,77)(72,81)(74,88)(75,86)(76,90)(78,94)(79,84)(80,96)(82,99)(83,98)(85,89)(87,97)(91,100)(92,95)(93,101);(54,55,59,62)(56,61,64,69)(57,65,58,60)(63,68,66,67)(70,72)(71,76)(73,81)(74,87)(75,83)(77,90)(78,93)(79,91)(80,95)(82,89)(84,100)(85,99)(86,98)(88,97)(92,96)(94,101);(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)(55,60)(56,63)(57,58)(62,65)(64,66)(67,68)(70,71)(72,80,83,93)(73,84,86,77)(74,78)(75,79)(76,82,91,87)(81,96)(85,94,88,92)(89,95)(90,97)(98,101)(99,100)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,d^2=h,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^52,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,e^c=eg,f^c=fgh1028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62118);