Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×D29 |
| Fitting | C16×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D29 |
| commutator, hypocenter | C29 | C2×C16 |
| Frattini | C8 | C2×D29 |
| Fitting | C16×C29 | C2 |
| socle | C2×C29 | C2×C8 |
| prime radical | C2×D29 | C8 |
| cosocle | C8×C29 | C22 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C16 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D29, #14270996, C2×C16×D29, … |
| maximal normal subgroup of | C32×D29, #14270996, C2×C16×D29, … |
| maximal quotient of | C16×Dic29, #14270942, #14270981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 4);