Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C43 · Schur multiplier (H2) = C1 |
| direct product | M32×C43 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C43 | C22 |
| commutator | C2 | C2×C8×C43 |
| Frattini, cosocle | C8 | C22×C43 |
| socle | C2×C43 | C2×C8 |
| prime radical | C22×C43 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C43 ◁ G | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 688 |
A minimal faithful permutation representation — 2 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59);(2,10)(4,12)(6,14)(8,16)860 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 17);