Finite Group DatabasebetaFinite Group Databasebeta| order | 6928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic866 |
| unambiguous semidirect product | (C2×C433)⋊Q8 |
| Sylow | C433 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D433 |
| commutator | C2×C433 | C23 |
| Frattini | C2 | C22×D433 |
| Fitting | C2×C4×C433 | C2 |
| socle | C22×C433 | C22 |
| hypercenter | C2×C4 | D433 |
| hypocenter | C433 | C2×Q8 |
| LCS | G ▷ C2×C433 ▷ C433 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
38 conjugacy classes of subgroups.
1738 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28357138, #28357143, #28357145, … |
| maximal normal subgroup of | #28357138, #28357143, #28357145, … |
| maximal quotient of | C2×#20294076, C2×C4⋊Dic433, C4×Dic866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6928, 38);