Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#20272918 |
| Sylow | C53 ⋊ C2×#1425 |
182 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 107 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 — 3 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)(56,58,70,97,61,73,78,85,60,72,89,113,81,103,80,102,63,75,99,118,83,105,79,101,62,74,98,117,77,100,59,71)(57,64,76,95,67,87,108,106,84,112,110,119,111,115,91,96,68,88,109,116,92,114,90,94,66,86,107,104,82,93,65,69);(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)(56,57,60,66,63,68,62,84)(58,69,72,94,75,96,74,106)(59,76,78,107,80,109,79,110)(61,82,81,92,83,111,77,67)(64,85,86,102,88,101,112,71)(65,89,90,99,91,98,108,70)(73,104,103,116,105,119,100,95)(87,97,93,113,114,118,115,117);(54,55)1220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90078);