Finite Group DatabasebetaFinite Group Databasebeta| order | 10928 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C683⋊C16 |
| derived, Sylow | C683 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D683 |
| commutator, hypocenter | C683 | C16 |
| Fitting, cosocle | C8×C683 | C2 |
| socle, prime radical | C2×C683 | C8 |
| LCS | G ▷ C683 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,683|a^2=b,b^2=c,c^2=d,e^a=e^6822744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D683, C2×C683⋊C16, #36345955, … |
| maximal normal subgroup of | C16×D683, C2×C683⋊C16, #36345955, … |
| maximal quotient of | C683⋊C32, C2×C683⋊C16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10928, 15);