Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#20272907 |
| Sylow | C53 ⋊ C2×#1420 |
286 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 286 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)(56,58,63,74)(57,64,68,90)(59,76,81,105)(60,73,62,71)(61,83,85,103)(65,92,95,101)(66,96,86,88)(67,97,98,99)(69,75,102,112)(70,79,106,116)(72,77,108,84)(78,114,80,113)(82,89,93,118)(87,91,104,115)(94,107,111,119)(100,117,109,110);(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)(56,57,60,66,63,68,62,86)(58,69,71,100,74,102,73,109)(59,75,78,110,81,112,80,117)(61,82,77,98,85,93,84,67)(64,87,88,70,90,104,96,106)(65,91,94,116,95,115,111,79)(72,107,103,92,108,119,83,101)(76,97,113,118,105,99,114,89);(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, 90038);