Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #10669 |
296 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 91 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)(54,56,59,67)(55,61,63,69)(57,66,58,65)(60,68,62,64)(70,73)(71,77)(72,80)(74,86)(75,84)(76,88)(78,93)(79,92)(81,98)(82,96)(83,94)(85,87)(89,100)(90,91)(95,101)(97,99);(55,60)(56,65)(57,58)(61,69)(62,63)(66,67)(70,72,74,81,75,82,87,99)(71,76,78,89,79,90,94,101)(73,80,86,98,84,96,85,97)(77,91,93,95,92,88,83,100);(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)(54,55,58,60,59,63,57,62)(56,64,66,69,67,68,65,61)(70,71)(72,76)(73,83,84,93)(74,78)(75,79)(77,85,92,86)(80,95,96,100)(81,89)(82,90)(87,94)(88,97,91,98)(99,101)Polycyclic presentation:
2^8,53|a^2=dg,b^2=de,c^2=g,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,f^a=fgh,i^a=i^52,c^b=cf,d^b=dg,e^b=eg,f^b=fg,d^c=dh,e^c=eh,f^c=fg1028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74595);