Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D53×#1425 |
| Fitting | C53×#1425 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1425 |
182 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 points:
(1,3,15,42,6,18,23,30,5,17,34,58,26,48,25,47,8,20,44,63,28,50,24,46,7,19,43,62,22,45,4,16)(2,9,21,40,12,32,53,51,29,57,55,64,56,60,36,41,13,33,54,61,37,59,35,39,11,31,52,49,27,38,10,14)(65,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67);(1,2,5,11,8,13,7,29)(3,14,17,39,20,41,19,51)(4,21,23,52,25,54,24,55)(6,27,26,37,28,56,22,12)(9,30,31,47,33,46,57,16)(10,34,35,44,36,43,53,15)(18,49,48,61,50,64,45,40)(32,42,38,58,59,63,60,62);(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)1064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90077);