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 ⋊ #11461 |
320 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 103 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)(54,57,58,65)(55,60,61,67)(56,63,64,69)(59,66,62,68)(72,80)(76,86)(81,92)(82,93)(87,96)(88,97)(94,100)(98,101);(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)(54,56)(55,59)(57,63)(58,64)(60,66)(61,62)(65,69)(67,68)(70,72)(71,76)(73,81)(74,82)(75,80)(77,87)(78,88)(79,86)(83,94)(84,92)(85,93)(89,98)(90,96)(91,97)(95,100)(99,101);(54,55)(56,62,64,59)(57,60)(58,61)(63,68,69,66)(65,67)(70,71,73,77,74,78,83,89,75,79,84,90,85,91,95,99)(72,76,81,87,82,88,94,98,80,86,92,96,93,97,100,101)Polycyclic presentation:
2^8,53|a^2=e,c^2=f,e^2=g,g^2=h,b^a=bd,d^a=df,c^b=ch,e^b=ef,i^b=i^522144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78772);