Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×D61⋊C8 |
| unambiguous semidirect product | D61⋊(C23×C8) |
| derived, Sylow | C61 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #6923 |
| commutator, hypocenter | C61 | C24×C8 |
| Frattini | C2 | C24×#6923 |
| Fitting | C23×C4×C61 | C4 |
| socle | C24×C61 | C2×C4 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C23×C4 | |
1976 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | #30602350, #30602353, #30602374, … |
| maximal normal subgroup of | #30602350, #30602353, #30602374, … |
| maximal quotient of | C23×C4×#92420, C22×C4×D61⋊C8, C22×D61⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21494);