Finite Group DatabasebetaFinite Group Databasebeta| order | 8336 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D521 |
| Fitting | C8×C521 ⋊ C2 |
| derived, Sylow | C521 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D521 |
| commutator, hypocenter | C521 | C2×C8 |
| Frattini | C4 | C2×D521 |
| Fitting | C8×C521 | C2 |
| socle | C2×C521 | C2×C4 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
2096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D521, #30659647, C2×C8×D521, … |
| maximal normal subgroup of | C16×D521, #30659647, C2×C8×D521, … |
| maximal quotient of | C8×Dic521, #30659620, #30659637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8336, 21);