Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #22277 |
826 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 259 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) = 13568 |
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)(58,61,62,59)(60,64,65,63)(67,74)(68,78)(73,89)(75,85)(77,81)(79,93)(80,94)(92,96);(58,60,62,65)(59,63,61,64)(66,69,71,83,70,82,84,97)(67,73,75,80,74,89,85,94)(68,77,79,92,78,81,93,96)(72,86,87,95,76,88,90,91);(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)(58,59,62,61)(60,64,65,63)(66,68)(67,72)(69,81)(70,78)(71,79)(73,88)(74,76)(75,87)(77,82)(80,91)(83,96)(84,93)(85,90)(86,89)(92,97)(94,95);(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)(54,55,57,56)(59,61)(63,64)(66,67)(68,76)(69,80)(70,74)(71,85)(72,78)(73,83)(75,84)(77,91)(79,87)(81,95)(82,94)(86,96)(88,92)(89,97)(90,93)Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,c^2=efh,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^52,c^b=ce,d^b=dh,i^b=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 183419);