Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1301 ⋊ C2 |
| Sylow | C53 ⋊ #10627 |
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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 — 3 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)(56,61)(59,60)(62,65,66,77,67,78,80,91)(63,69,70,83,71,84,86,93)(64,73,74,89,75,76,79,90)(68,81,72,87,82,92,85,88);(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)(56,58)(57,60)(59,61)(62,64)(63,68)(65,76)(66,79)(67,75)(69,81)(70,85)(71,82)(72,86)(73,78)(74,80)(77,89)(83,88)(84,92)(87,93)(90,91);(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)(62,63)(64,72,75,85)(65,69)(66,70)(67,71)(68,74,82,79)(73,88,76,87)(77,83)(78,84)(80,86)(81,90,92,89)(91,93)Polycyclic presentation:
2^8,53|a^2=e,c^2=d,d^2=g,f^2=h,b^a=bd,c^a=ce,f^a=fg,i^a=i^52,c^b=cf,d^b=dg,e^b=eg,f^b=fh,i^b=i^52,f^c=fgh1028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 74340);