Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #7252 |
344 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 95 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)(62,64,66,75)(63,68,70,81)(65,74,76,88)(67,73,78,87)(69,80,82,91)(71,72,84,86)(77,79,89,90)(83,85,92,93);(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)(57,60)(59,61)(62,63,65,69,67,71,77,83)(64,72,74,85,73,68,79,80)(66,70,76,82,78,84,89,92)(75,81,88,91,87,86,90,93)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=f,d^2=h,b^a=bc,c^a=cf,e^a=efg,c^b=cg,g^b=gh,i^b=i^52,e^c=eh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56693);