Finite Group DatabasebetaFinite Group Databasebeta| order | 8336 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#16861967 |
| derived, Sylow | C521 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #14523438 |
| commutator, hypocenter | C521 | C2×C8 |
| Frattini | C2 | C2×#14523438 |
| Fitting, socle | C22×C521 | C4 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C22 | |
22 conjugacy classes of subgroups.
536 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16861967, #30659763, C22⋊#16861967, … |
| maximal normal subgroup of | C4×#16861967, #30659763, C22⋊#16861967, … |
| maximal quotient of | C4×#16861967, C22⋊#16861967, C4⋊#16861967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8336, 47);