Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C32×#6923 |
| Fitting | C32×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #6923 |
| commutator, hypocenter | C61 | C4×C32 |
| Frattini | C16 | C2×#6923 |
| Fitting | C32×C61 | C4 |
| socle | C2×C61 | C4×C16 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | C64×#6923, #30595232, C2×C32×#6923, … |
| maximal normal subgroup of | C64×#6923, #30595232, C2×C32×#6923, … |
| maximal quotient of | C32×#92420, #92420⋊C32, (C2×#6923)⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19613);