Finite Group DatabasebetaFinite Group Databasebeta| order | 10928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D683 |
| unambiguous semidirect product | C683⋊C24 |
| unambiguous semidirect product | (C2×C683)⋊C23 |
| Fitting, socle | C23×C683 ⋊ C2 |
| derived, Sylow | C683 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D683 |
| commutator, cosocle, hypocenter | C683 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C683 | C2 |
| LCS | G ▷ C683 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
2744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D683, C2×(C2×D683)⋊C4, #36345984, … |
| maximal normal subgroup of | C22⋊C4×D683, C2×(C2×D683)⋊C4, #36345984, … |
| maximal quotient of | C22×C4×D683, C23×Dic683, C2×D4×D683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10928, 42);