Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #23470 |
1178 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 209 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 — 4 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)(62,66,67,78)(63,70,71,86)(64,73,74,90)(65,75,76,77)(68,80,81,93)(69,83,84,85)(72,87,88,89)(79,91,82,92);(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)(62,65,67,76)(63,69,71,84)(64,72,74,88)(66,77,78,75)(68,79,81,82)(70,85,86,83)(73,89,90,87)(80,92,93,91);(54,56,57,61)(55,58,59,60)(62,64)(63,68)(65,72)(66,73)(67,74)(69,82)(70,80)(71,81)(75,87)(76,88)(77,89)(78,90)(79,84)(83,92)(85,91)(86,93);(54,55,57,59)(56,60,61,58)(62,63)(64,68)(65,69)(66,70)(67,71)(72,82)(73,80)(74,81)(75,83)(76,84)(77,85)(78,86)(79,88)(87,92)(89,91)(90,93)Polycyclic presentation:
2^8,53|a^2=e,b^2=e,c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,d^c=dh,i^d=i^52722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 196984);