Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C53 ⋊ #8780 |
310 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 123 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)(62,65)(63,69,70,82)(64,73)(66,77)(67,78)(68,80,72,84)(71,76,83,91)(74,87)(75,88)(79,92)(81,90,85,86)(89,93);(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)(62,64,66,74,67,75,79,89)(63,68,71,81,70,72,83,85)(65,73,77,87,78,88,92,93)(69,80,76,90,82,84,91,86);(54,55,56,58,57,59,60,61)(62,63)(64,72,75,68)(65,76,78,91)(66,71)(67,70)(69,77,82,92)(73,86)(74,85,89,81)(79,83)(80,87)(84,93)(88,90)Polycyclic presentation:
2^8,53|a^2=f,b^2=e,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,f^b=fg,i^b=i^52,f^c=fg1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 63212);