Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #9331 |
438 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 91 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)(55,60)(56,62)(58,65)(59,66)(61,64)(63,68)(67,69)(70,73)(71,78)(72,82)(74,87)(75,86)(76,88)(77,91)(79,95)(80,94)(81,96)(83,100)(84,99)(85,89)(90,98)(92,101)(93,97);(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)(55,59,61,67)(57,62)(58,63)(60,66,64,69)(65,68)(70,72,74,83,76,84,75,90)(71,77,79,81,80,93,89,92)(73,82,87,100,88,99,86,98)(78,91,95,96,94,97,85,101);(54,55)(56,59,63,67)(57,64,65,60)(58,61)(62,66)(68,69)(70,71)(72,81)(73,85,88,95)(74,89)(75,79)(76,80)(77,83)(78,87,94,86)(82,97,99,91)(84,92)(90,93)(96,98,101,100)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,d^2=gh,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=egh,f^c=fg866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 66517);