Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#3152 ⋊ C2 |
| Sylow | C53 ⋊ #18996 |
948 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 155 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 — 4 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)(62,66,68,67)(63,71,73,72)(64,76,77,80)(65,78,79,81)(69,74,83,86)(70,84,85,87)(75,90,92,91)(82,88,93,89);(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)(56,61)(57,59)(58,60)(62,65)(63,70)(64,75)(66,78)(67,81)(68,79)(69,82)(71,84)(72,87)(73,85)(74,88)(76,90)(77,92)(80,91)(83,93)(86,89);(56,60)(58,61)(62,64)(63,69)(65,75)(66,76)(67,80)(68,77)(70,82)(71,74)(72,86)(73,83)(78,90)(79,92)(81,91)(84,88)(85,93)(87,89);(55,58)(56,60)(59,61)(62,63,68,73)(64,74,77,86)(65,70,79,85)(66,72,67,71)(69,80,83,76)(75,89,92,88)(78,87,81,84)(82,90,93,91)Polycyclic presentation:
2^8,53|a^2=g,d^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fgh,e^b=eg,f^b=fh,e^c=eh,f^c=fgh,i^c=i^52866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 150813);