Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C25×#6923 |
| unambiguous semidirect product | D61⋊(C24×C4) |
| Fitting, socle | C25×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #6923 |
| commutator, hypocenter | C61 | C25×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C61 | C4 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C25 | |
10552 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460992, #379×#6923, #30609633, … |
| maximal normal subgroup of | C2×#21460992, #379×#6923, #30609633, … |
| maximal quotient of | C24×C4×#6923, C24×C22⋊#6923, C24×C4⋊#6923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21507);