Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #9195 |
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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 — 3 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)(62,65)(63,69)(64,73)(66,80)(67,77)(68,81)(70,76)(71,87)(72,78)(74,88)(75,90)(79,89)(82,93)(83,91)(84,85)(86,92);(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)(56,61)(59,60)(62,64,72,75,67,74,66,79)(63,68,71,86,70,83,85,82)(65,73,78,90,77,88,80,89)(69,81,87,92,76,91,84,93);(54,55,56,59,57,60,61,58)(62,63,66,71,67,70,72,85)(64,68,75,82,74,83,79,86)(65,76,78,87,77,69,80,84)(73,81,89,92,88,91,90,93)Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,d^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,f^c=fg1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 65589);