Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C29 · Schur multiplier (H2) = C22 |
| direct product | C29×#137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C23×C29 |
| prime radical | #41×C29 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 464 |
A minimal faithful permutation representation — 3 generators on 45 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)(32,38)(33,41)(34,36)(35,39)(37,43)(40,45)(42,44);(30,32,34,40)(31,35,36,44)(33,42,43,39)(37,45,41,38);(31,36)(35,44)(37,41)(38,45)319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 198);