Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×#16840601 |
| derived, Sylow | C61 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #6923 |
| commutator, hypocenter | C61 | C2×C64 |
| Frattini | C16 | C2×#6923 |
| Fitting | C2×C16×C61 | C4 |
| socle | C22×C61 | C32 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C16 | |
40 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16840601, #30595231, #30595233, … |
| maximal normal subgroup of | C4×#16840601, #30595231, #30595233, … |
| maximal quotient of | C4×#16840601, C22⋊#16840601, C4⋊#16840601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19677);