Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #12897 |
278 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 278 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) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 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)(62,65,66,67,68,82,83,84)(63,70,71,89,74,73,72,80)(64,76,77,91,79,81,92,78)(69,85,75,90,87,88,86,93);(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)(62,64,68,79)(63,69)(65,81,82,76)(66,77,83,92)(67,78,84,91)(70,88)(71,75)(72,86)(73,85)(74,87)(80,90)(89,93);(54,55,56,58,57,59,60,61)(62,63,67,73,66,72,82,89,68,74,84,70,83,71,65,80)(64,75,78,90,77,69,76,85,79,86,91,93,92,87,81,88)Polycyclic presentation:
2^8,53|a^2=f,b^2=de,c^2=d,d^2=h,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=ch,f^c=fh,i^c=i^521520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85975);