Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C53 · Schur multiplier (H2) = C2×C42 |
| direct product | C53×#7959 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#95 |
| commutator | C2×C4 | C2×C42×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C24×C53 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C42×C53 ◁ G | |
634 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 77 points:
(2,6)(3,4)(7,8)(9,10)(11,17,18,14)(12,16)(13,15)(19,23,24,21)(20,22)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(1,2,4,8,5,7,3,6)(9,11,12,19,13,18,20,24)(10,14,16,21,15,17,22,23);(2,7)(6,8)(11,18)(14,17)(19,24)(21,23)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 947);