Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#6597 |
| derived, Sylow | C29 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D29 |
| commutator, hypocenter | C29 | C4×C8 |
| Frattini | C2×C4 | C2×D29 |
| Fitting | C42×C29 | C2 |
| socle, prime radical | C22×C29 | C2×C4 |
| cosocle | C2×C4×C29 | C22 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C42 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#6597, #14270884, #14270885, … |
| maximal normal subgroup of | C8×#6597, #14270884, #14270885, … |
| maximal quotient of | C8×#6597, #14270884, #14270918, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 9);