Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20277031 |
| Fitting | C2×C53×SD64 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2264 |
462 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 462 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)(57,64)(63,85)(65,88)(66,89)(67,83)(68,95)(73,94)(79,113)(86,115)(87,93)(90,116)(91,104)(92,117)(96,103)(100,119)(105,111);(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)(56,58,62,72)(57,63,64,85)(59,74,78,108)(60,80,82,114)(61,84,81,71)(65,90,88,116)(66,92,89,117)(67,93,83,87)(68,94,95,73)(69,97,99,76)(70,101,102,75)(77,112,110,107)(79,86,113,115)(91,119,104,100)(96,105,103,111)(98,109,106,118);(56,57)(58,68)(59,73)(60,79)(61,83)(62,64)(63,69)(65,76)(66,75)(67,81)(70,100)(71,103)(72,95)(74,92)(77,111)(78,94)(80,90)(82,113)(84,96)(85,99)(86,107)(87,106)(88,97)(89,101)(91,118)(93,98)(102,119)(104,109)(105,110)(108,117)(112,115)(114,116);(54,55)1040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 327705);