Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#1275 ⋊ C2 |
| Sylow | C53 ⋊ #8603 |
368 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 101 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)(56,62)(59,65)(63,68)(66,69)(70,73)(71,77)(72,81)(74,85)(75,86)(76,89)(78,91)(79,84)(80,92)(82,95)(83,96)(87,99)(88,100)(90,98)(93,94)(97,101);(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)(55,59)(57,63)(58,62)(60,66)(61,65)(64,68)(67,69)(70,72,74,82,75,83,88,97)(71,76,78,80,79,90,87,93)(73,81,85,95,86,96,100,101)(77,89,91,92,84,98,99,94);(54,55,57,60,58,61,64,67)(56,59,63,66,62,65,68,69)(70,71)(72,80)(73,84,86,77)(74,87)(75,79)(76,82)(78,88)(81,94,96,92)(83,93)(85,91,100,99)(89,95,98,101)(90,97)Polycyclic presentation:
2^8,53|a^2=f,b^2=d,d^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=ch,i^b=i^52,f^c=fg,i^c=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62436);