Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D29⋊C16 |
| derived, Sylow | C29 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #1181 |
| commutator, hypocenter | C29 | C2×C16 |
| Frattini | C4 | C2×#1181 |
| Fitting | C8×C29 | C4 |
| socle | C2×C29 | C2×C8 |
| prime radical | C2×D29 | C8 |
| cosocle | #6597 | C22 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^5,29|a^2=c,b^2=d,c^2=d,d^2=e,f^a=f^12,f^c=f^2888 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#1181, #14272050, #14272075, … |
| maximal normal subgroup of | C16×#1181, #14272050, #14272075, … |
| maximal quotient of | #14272049, #14272058, #14272084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 64);