Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #7155 |
222 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 2 generators on 93 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)(62,64,66,75,79,90,80,91,68,77,65,74,67,76,82,92)(63,69,70,73,83,87,81,93,72,85,86,89,71,84,78,88);(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)(54,55,56,58,57,59,60,61)(62,63)(64,73)(65,78)(66,81)(67,83)(68,72)(69,74)(70,80)(71,79)(75,85)(76,93)(77,89)(82,86)(84,92)(87,91)(88,90)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fh,d^2=g,e^2=fh,f^2=h,b^a=bc,c^a=cf,e^a=efh,f^a=fh,i^b=i^521544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56439);