Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×#92420 |
| derived, Sylow | C61 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #6923 |
| commutator, hypocenter | C61 | C24×C8 |
| Frattini | C2 | C24×#6923 |
| Fitting, socle | C25×C61 | C4 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C25 | |
1976 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | #30602352, C22×#16840628, C2×#21461485, … |
| maximal normal subgroup of | #30602352, C22×#16840628, C2×#21461485, … |
| maximal quotient of | C23×C4×#92420, C23×C22⋊#92420, C23×C4⋊#92420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21493);