Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C23×#11758217 |
| Sylow | C61 ⋊ C23×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×#6923 |
| commutator | C2×C61 | C24×C4 |
| Frattini | C2 | C24×#6923 |
| Fitting | C25×C61 | C4 |
| socle | C24×C61 | C2×C4 |
| hypercenter | C25 | #6923 |
| hypocenter | C61 | C23×M16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C25 | |
1720 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #30602356, #30602394, #30602424, … |
| maximal normal subgroup of | #30602356, #30602394, #30602424, … |
| maximal quotient of | C23×#14519832, C22×C4×#11758217, C23×C22⋊#92420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21495);