Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11641 |
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 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) = 6784 |
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)(54,57,59,58)(55,61,62,67)(56,64,66,65)(60,63,68,69)(70,73,75,76)(71,78,79,81)(72,83,85,86)(74,87,89,90)(77,91,82,93)(80,94,95,97)(84,98,88,99)(92,100,96,101);(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)(54,56,59,66)(55,60,62,68)(57,65,58,64)(61,69,67,63)(70,72,75,85)(71,77,79,82)(73,86,76,83)(74,88,89,84)(78,93,81,91)(80,96,95,92)(87,98,90,99)(94,100,97,101);(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)(54,55)(56,63)(57,61)(58,67)(59,62)(60,65)(64,68)(66,69)(70,71,74,80,76,81,90,97,75,79,89,95,73,78,87,94)(72,82,84,96,83,93,98,101,85,77,88,92,86,91,99,100)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=f,d^2=fh,e^2=g,g^2=h,b^a=bd,d^a=df,i^a=i^52,c^b=cf,d^b=dfh,e^b=eh,i^b=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79528);