Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #7327 |
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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 — 2 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)(54,56,57,64,58,63,65,69)(55,59,61,66,60,62,67,68)(70,72)(71,76)(73,81,85,98)(74,86)(75,83)(77,80,92,96)(78,93)(79,90)(82,87)(84,88,99,97)(89,94)(91,100,101,95);(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)(56,62,63,59)(57,61)(58,60)(64,68,69,66)(65,67)(70,71,74,78,75,79,87,94)(72,80,82,95,83,96,86,100)(73,77,84,91,85,92,99,101)(76,88,89,81,90,97,93,98)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=h,d^2=h,e^2=f,b^a=bc,c^a=cf,e^a=egh,i^a=i^52,c^b=cg,d^b=dfh,g^b=gh,e^c=eh866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56892);