Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #7223 |
192 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 2 generators on 85 points:
(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)(54,56,57,64,58,63,65,69)(55,59,61,66,60,62,67,68)(70,72,73,78,74,81,82,79,75,76,83,77,84,80,85,71);(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)(54,55)(56,62,63,59)(57,61)(58,60)(64,68,69,66)(65,67)(70,71,74,77,75,79,84,78)(72,73,80,82,76,83,81,85)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fgh,d^2=h,e^2=f,f^2=h,b^a=bc,c^a=cf,e^a=efg,f^a=fh,c^b=ch,d^b=dg,i^b=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56622);