Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#1960 ⋊ C2 |
| Sylow | C53 ⋊ #25609 |
1052 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1052 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)(58,60,61,65)(59,63,62,64)(68,77)(72,85)(76,91)(78,90)(84,96)(86,93)(89,97)(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)(66,69,80,87,71,82,70,81)(67,73,83,94,75,88,74,79)(68,76,90,95,77,91,78,92)(72,84,93,97,85,96,86,89);(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)(56,57)(59,62)(63,64)(66,68)(67,72)(69,76)(70,78)(71,77)(73,84)(74,86)(75,85)(79,89)(80,90)(81,92)(82,91)(83,93)(87,95)(88,96)(94,97);(58,59)(60,64)(61,62)(63,65)(66,67,71,75)(68,72,77,85)(69,79,82,94)(70,83,80,74)(73,87,88,81)(76,89,91,97)(78,93,90,86)(84,95,96,92)Polycyclic presentation:
2^8,53|a^2=h,c^2=fh,d^2=e,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=cg,d^b=dh,i^b=i^52,i^c=i^52878 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 223187);