Finite Group DatabasebetaFinite Group Databasebeta| order | 10928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C683⋊C8 |
| unambiguous semidirect product | (C2×C683)⋊C8 |
| derived, Sylow | C683 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D683 |
| commutator, hypocenter | C683 | C2×C8 |
| Frattini | C4 | C2×D683 |
| Fitting | C2×C4×C683 | C2 |
| socle, prime radical | C22×C683 | C4 |
| cosocle | C4×C683 | C22 |
| LCS | G ▷ C683 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
2744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic683, C4×C683⋊C8, #36345926, … |
| maximal normal subgroup of | C8×Dic683, C4×C683⋊C8, #36345926, … |
| maximal quotient of | C4×C683⋊C8, C22⋊(C683⋊C8), C4⋊(C683⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10928, 22);