Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#20276553 |
| Fitting | C2×C4×C16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2170 |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 87 points:
(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)(56,59,61,68,60,73,75,79,62,74,77,81,76,87,80,63)(57,58,65,70,66,71,83,85,67,72,84,86,64,69,82,78);(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)(57,63)(59,65)(60,71)(61,70)(62,72)(64,81)(66,68)(67,79)(69,76)(73,83)(74,84)(75,85)(77,86)(78,80)(82,87);(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)(56,57,61,65,60,66,75,83,62,67,77,84,76,64,80,82)(58,68,70,73,71,79,85,74,72,81,86,87,69,63,78,59);(54,55)3440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322797);