Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ C4×#368 |
314 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 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)(54,56,57,55);(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)(58,60,62,70,63,72,74,71)(59,64,66,77,67,79,81,78)(61,73,75,69,76,86,88,87)(65,80,82,68,83,84,89,85);(54,55,57,56)(58,59,61,65,74,81,88,89,63,67,76,83,62,66,75,82)(60,68,69,77,70,84,86,79,72,85,87,78,71,80,73,64)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=deg,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,d^b=dg,e^b=eg,g^b=gh,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, 84979);