Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D53×SD128 |
| Fitting | C53×SD128 ⋊ C2 |
| Sylow | C53 ⋊ C2×SD128 |
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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:
(2,8)(3,14)(4,15)(5,20)(6,24)(9,10)(11,39)(12,41)(13,30)(16,47)(17,50)(18,31)(19,27)(21,55)(22,35)(23,28)(25,38)(26,29)(32,52)(33,51)(34,37)(36,57)(40,64)(42,43)(44,48)(45,46)(49,63)(53,60)(54,59)(56,62)(58,61)(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);(1,2,7,13)(3,8,18,30)(4,19,22,53)(5,23,25,56)(6,26,24,12)(9,31,34,14)(10,35,37,15)(11,38,40,20)(16,39,49,64)(17,41,48,29)(21,54,45,52)(27,58,60,43)(28,61,62,42)(32,63,59,47)(33,44,57,50)(36,46,51,55);(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)980 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90612);