Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | C53×#1452 ⋊ C2 |
| Sylow | C53 ⋊ #8158 |
400 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 135 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)(55,60)(59,65)(61,67)(66,69)(70,73,74,84,75,85,86,97)(71,77,78,90,79,91,92,100)(72,81,83,96,82,95,87,98)(76,88,89,99,80,93,94,101);(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)(54,56,57,62,58,63,64,68)(55,59,61,66,60,65,67,69)(70,72)(71,76,79,80)(73,81)(74,83)(75,82)(77,88,91,93)(78,89,92,94)(84,96)(85,95)(86,87)(90,99,100,101)(97,98);(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)(56,59)(57,61)(58,60)(62,66)(63,65)(64,67)(68,69)(70,71,74,78,75,79,86,92)(72,80,83,94,82,76,87,89)(73,77,84,90,85,91,97,100)(81,93,96,101,95,88,98,99)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,e^2=g,f^2=h,b^a=bd,c^a=ch,f^a=fg,i^a=i^52,d^b=dg,i^b=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 60107);