Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20277021 |
| Fitting | C2×C53×D32 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2262 |
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 119 points:
(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)(56,59,62,77)(57,64,68,67)(58,70,74,73)(60,75,81,108)(61,76,84,109)(63,85,87,95)(65,88,92,91)(66,89,94,82)(69,96,97,104)(71,98,101,100)(72,99,103,83)(78,105,111,110)(79,106,113,112)(80,107,114,117)(86,93,115,119)(90,102,116,118);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(56,58)(57,63)(59,70)(60,79)(61,83)(62,74)(64,85)(65,90)(66,93)(67,95)(68,87)(69,78)(71,80)(72,76)(73,77)(75,106)(81,113)(82,86)(84,99)(88,102)(89,115)(91,118)(92,116)(94,119)(96,105)(97,111)(98,107)(100,117)(101,114)(103,109)(104,110)(108,112);(56,57)(58,69)(59,64)(60,78)(61,82)(62,68)(63,71)(65,80)(66,76)(67,77)(70,96)(72,102)(73,104)(74,97)(75,105)(79,93)(81,111)(83,90)(84,89)(85,98)(86,112)(87,101)(88,107)(91,117)(92,114)(94,109)(95,100)(99,116)(103,118)(106,115)(108,110)(113,119);(54,55)1064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 327693);