Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×Q32 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C29 | D8 |
| commutator, Frattini, cosocle | C8 | C22×C29 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C4×C29 ◁ C8×C29 ◁ G | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 928 |
A minimal faithful permutation representation — 2 generators on 61 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)(46,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47);(30,46,38,54)(31,47,39,55)(32,48,40,56)(33,49,41,57)(34,50,42,58)(35,51,43,59)(36,52,44,60)(37,53,45,61)319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 63);