Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #23943 |
1158 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 97 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)(59,63)(62,64)(68,77)(72,86)(76,91)(78,93)(85,96)(87,94)(90,97)(92,95);(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)(55,57)(66,69,71,81)(67,73,75,88)(68,76,77,91)(70,83,84,80)(72,85,86,96)(74,89,82,79)(78,95,93,92)(87,97,94,90);(54,55)(56,57)(58,60,61,65)(59,62,63,64)(66,68)(67,72)(69,76)(70,78)(71,77)(73,85)(74,87)(75,86)(79,90)(80,92)(81,91)(82,94)(83,95)(84,93)(88,96)(89,97);(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)(58,59)(60,64)(61,63)(62,65)(66,67,71,75)(68,72,77,86)(69,79,81,89)(70,82,84,74)(73,83,88,80)(76,90,91,97)(78,94,93,87)(85,95,96,92)Polycyclic presentation:
2^8,53|a^2=h,b^2=e,c^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^52,c^b=cg,d^b=dh,f^c=fh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 201537);