Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #8783 |
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 101 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)(56,63)(59,62)(64,66)(67,69)(70,73)(71,77,78,90)(72,81)(74,85)(75,86)(76,88,80,92)(79,84,91,99)(82,95)(83,96)(87,100)(89,98,93,94)(97,101);(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)(54,56)(55,59)(57,63)(58,64)(60,62)(61,67)(65,66)(68,69)(70,72,74,82,75,83,87,97)(71,76,79,89,78,80,91,93)(73,81,85,95,86,96,100,101)(77,88,84,98,90,92,99,94);(54,55,58,61,57,60,65,68)(56,62,64,69,63,59,66,67)(70,71)(72,80,83,76)(73,84,86,99)(74,79)(75,78)(77,85,90,100)(81,94)(82,93,97,89)(87,91)(88,95)(92,101)(96,98)Polycyclic presentation:
2^8,53|a^2=f,b^2=e,c^2=dh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,c^b=ch,f^b=fg,i^b=i^52,f^c=fg1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 63224);