Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#3147 ⋊ C2 |
| Sylow | C53 ⋊ #18686 |
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 77 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)(62,65,67,66)(63,70,71,69)(64,73,75,74)(68,72,77,76);(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)(56,61)(57,59)(58,60)(63,69)(65,66)(68,76)(70,71)(72,77)(73,74);(56,60)(58,61)(62,64)(63,68)(65,73)(66,74)(67,75)(69,76)(70,72)(71,77);(55,58)(56,60)(59,61)(62,63)(64,72)(65,70)(66,69)(67,71)(68,74)(73,77)(75,76)Polycyclic presentation:
2^8,53|d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,e^b=eg,f^b=fh,d^c=dg,e^c=eh,f^c=fh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 147394);