Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7066 |
176 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 47 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) = 3392 |
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)(55,58,60,59)(62,64,67,72)(63,68)(65,73,75,85)(66,74,77,86)(69,79)(70,83)(71,80)(76,87,88,93)(78,81)(82,90)(84,92)(89,91);(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)(56,59,61,58)(57,60)(62,63,65,70,66,71,76,84,67,69,75,81,77,82,88,91)(64,68,73,78,74,80,87,89,72,79,85,83,86,90,93,92)Polycyclic presentation:
2^8,53|a^2=d,b^2=eg,c^2=gh,d^2=f,f^2=h,b^a=bc,c^a=ce,e^a=eg,c^b=ch,d^b=degh,i^b=i^52,d^c=dg1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56211);