Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C53 ⋊ #12511 |
260 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 75 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) = 6784 |
A minimal faithful permutation representation — 3 generators on 101 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)(55,60)(59,67)(61,65)(62,68)(70,73,74,90,77,88,75,91,78,93,95,89,76,92,87,72)(71,80,81,98,84,101,82,79,85,86,96,99,83,97,94,100);(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)(54,56,57,63,58,64,66,69)(55,59,61,62,60,67,65,68)(70,72,87,92,76,89,95,93,78,91,75,88,77,90,74,73)(71,79,94,101,83,98,96,80,85,100,82,97,84,99,81,86);(54,55)(56,62)(57,65)(58,60)(59,63)(61,66)(64,68)(67,69)(70,71)(72,86)(73,79)(74,94)(75,96)(76,84)(77,83)(78,85)(80,91)(81,87)(82,95)(88,98)(89,97)(90,101)(92,99)(93,100)Polycyclic presentation:
2^8,53|b^2=dgh,c^2=ef,d^2=fh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,g^a=gh,i^c=i^521058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84260);