Finite Group DatabasebetaFinite Group Databasebeta| order | 8168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D1021 |
| unambiguous semidirect product | C1021⋊C23 |
| unambiguous semidirect product | (C2×C1021)⋊C22 |
| Fitting, socle | C22×C1021 ⋊ C2 |
| derived, Sylow | C1021 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D1021 |
| commutator, hypocenter | C1021 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C1021 | C2 |
| LCS | G ▷ C1021 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
2048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30654700, C2×C4×D1021, D4×D1021, … |
| maximal normal subgroup of | #30654700, C2×C4×D1021, D4×D1021, … |
| maximal quotient of | C2×C4×D1021, C22×Dic1021, D4×D1021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8168, 12);