Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #7393 |
110 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 59 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) = 13568 |
A minimal faithful permutation representation — 2 generators on 93 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)(54,55,57,59)(56,61,60,58)(62,64,66,68)(63,69,70,73)(65,76,77,74)(67,75,79,80)(71,85,83,81)(72,82,84,87)(78,89,90,88)(86,93,92,91);(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)(56,60)(59,61)(62,63,65,71,67,72,78,86,68,69,76,81,80,82,89,91,66,70,77,83,79,84,90,92,64,73,74,85,75,87,88,93)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=eh,d^2=f,f^2=g,g^2=h,b^a=bc,c^a=ce,i^a=i^52,c^b=ceh,d^b=dh1532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57048);