Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C29 · Schur multiplier (H2) = C2 |
| direct product | C29×C4⋊C8 |
| unambiguous semidirect product | C4⋊(C8×C29) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C22 |
| commutator | C2 | C2×C8×C29 |
| Frattini, cosocle | C2×C4 | C22×C29 |
| socle, prime radical | C22×C29 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ G | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 928 |
A minimal faithful permutation representation — 2 generators on 41 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)(31,33)(34,35,36,38,37,39,40,41);(30,31,32,33)580 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 55);