Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#2162 ⋊ C2 |
| Sylow | C53 ⋊ #11490 |
364 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 111 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:
(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)(62,65,66,80,68,81,69,67)(63,71,82,90,74,89,72,73)(64,76,83,92,79,84,77,78)(70,85,75,91,87,93,88,86);(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)(55,58)(56,60)(62,64)(63,70)(65,76)(66,83)(67,78)(68,79)(69,77)(71,85)(72,88)(73,86)(74,87)(75,82)(80,92)(81,84)(89,93)(90,91);(54,55,56,59,57,58,60,61)(62,63,67,73,69,72,81,89,68,74,80,90,66,82,65,71)(64,75,78,85,77,70,84,86,79,88,92,93,83,87,76,91)Polycyclic presentation:
2^8,53|a^2=e,c^2=fg,d^2=h,e^2=g,g^2=h,b^a=bd,d^a=df,d^b=dh,e^b=efh,i^b=i^522156 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78894);