Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#1313 ⋊ C2 |
| Sylow | C53 ⋊ #11405 |
282 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 143 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) = 6784 |
A minimal faithful permutation representation — 3 generators on 93 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)(64,73)(68,81)(72,87)(74,76)(75,89)(80,90)(82,83)(88,91);(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)(54,55,56,58,57,59,60,61)(62,64)(63,68,70,81)(65,76)(66,75)(67,73)(69,83,84,82)(71,72,86,87)(74,78)(77,80)(79,89)(85,91,93,88)(90,92);(62,63,65,69,66,71,77,85,67,70,78,84,79,86,92,93)(64,72,74,88,75,81,90,83,73,87,76,91,89,68,80,82)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=f,e^2=g,f^2=h,b^a=bf,e^a=eh,c^b=ch,d^b=dh,i^c=i^521232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78571);