Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#20275264 |
| Fitting | C22×#101×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1915 |
1670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 87 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)(57,63)(58,67)(60,74)(61,71)(62,75)(64,70)(65,81)(66,72)(68,82)(69,84)(73,83)(76,87)(77,85)(78,79)(80,86);(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)(56,58,66,69,61,68,60,73)(57,62,65,80,64,77,79,76)(59,67,72,84,71,82,74,83)(63,75,81,86,70,85,78,87);(56,57,60,65,61,64,66,79)(58,62,69,76,68,77,73,80)(59,70,72,81,71,63,74,78)(67,75,83,86,82,85,84,87);(54,55)1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 171594);