Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#20275820 |
| Fitting | C2×C53×#338 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2017 |
1938 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1938 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 87 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)(56,59)(57,64)(58,68)(60,74)(61,75)(62,76)(63,78)(65,82)(66,83)(67,84)(69,73)(70,87)(71,86)(72,77)(79,81)(80,85);(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)(56,58)(57,63)(59,73)(60,70)(61,69)(62,71)(64,81)(65,79)(66,80)(67,77)(68,74)(72,78)(75,86)(76,87)(82,85)(83,84);(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)(56,57)(58,67)(59,72)(60,77)(61,65)(62,66)(63,69)(64,75)(68,85)(70,80)(71,79)(73,84)(74,83)(76,82)(78,86)(81,87);(54,55)1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 196745);