Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7058 |
354 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 51 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:
(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)(55,58)(59,60)(62,64)(63,69)(65,78)(66,80)(67,75)(68,77)(70,86)(71,88)(72,74)(73,85)(76,82)(79,92)(81,83)(84,90)(87,91)(89,93);(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)(54,55)(56,60,61,58)(57,59)(62,63,66,71,67,72,81,89,68,73,82,90,65,70,79,87)(64,74,76,91,75,85,92,88,77,86,80,93,78,69,83,84)Polycyclic presentation:
2^8,53|a^2=d,c^2=h,d^2=f,f^2=h,b^a=bc,c^a=ce,e^a=eg,i^a=i^52,c^b=ch,d^b=deh,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, 56195);