Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C43 · Schur multiplier (H2) = C1 |
| direct product | Q32×C43 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C43 | D8 |
| commutator, Frattini, cosocle | C8 | C22×C43 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C4×C43 ◁ C8×C43 ◁ G | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 1376 |
A minimal faithful permutation representation — 2 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18)(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);(1,17,9,25)(2,18,10,26)(3,19,11,27)(4,20,12,28)(5,21,13,29)(6,22,14,30)(7,23,15,31)(8,24,16,32)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 20);