Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1633 ⋊ C2 |
| Sylow | C53 ⋊ #18685 |
930 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 149 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) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(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)(65,76)(69,83)(73,87)(77,89)(81,92)(84,90)(86,93)(88,91);(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)(54,55)(56,61)(57,59)(58,60)(62,65)(63,69)(64,73)(66,77)(67,76)(68,81)(70,84)(71,83)(72,86)(74,88)(75,87)(78,90)(79,91)(80,89)(82,92)(85,93);(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)(56,60)(58,61)(62,64,67,75)(63,68,71,82)(65,73,76,87)(66,79,80,74)(69,81,83,92)(70,85,78,72)(77,91,89,88)(84,93,90,86);(55,58)(56,60)(59,61)(62,63,67,71)(64,72,75,85)(65,69,76,83)(66,78,80,70)(68,79,82,74)(73,86,87,93)(77,90,89,84)(81,91,92,88)Polycyclic presentation:
2^8,53|a^2=g,b^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,i^b=i^52,d^c=dg,e^c=eh,f^c=fh,i^c=i^52,i^d=i^52716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 147389);