Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#20276730 |
| Fitting | C2×C53×#354 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2201 |
1136 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1136 conjugacy classes of subgroups — too many to draw. Only its 155 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:
(3,6,8,19)(4,10,12,26)(5,14,16,17)(7,20,21,18)(9,22,23,24)(11,25,27,34)(13,28,29,33)(15,31,32,30)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86);(3,5,8,16)(4,9,12,23)(6,17,19,14)(7,15,21,32)(10,24,26,22)(11,13,27,29)(18,31,20,30)(25,33,34,28)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87);(3,4)(5,13)(6,10)(7,11)(8,12)(9,15)(14,28)(16,29)(17,33)(18,25)(19,26)(20,34)(21,27)(22,30)(23,32)(24,31)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87);(1,2)710 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323613);