Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×Dic61 |
| derived, Sylow | C61 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D61 |
| commutator, hypocenter | C61 | C23×C42 |
| Frattini | C22 | C24×D61 |
| Fitting | C24×C4×C61 | C2 |
| socle | C25×C61 | C22 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C24×C4 | |
3000 conjugacy classes of subgroups.
2048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29567932, #29585230, #29585254, … |
| maximal normal subgroup of | #29567932, #29585230, #29585254, … |
| maximal quotient of | C22×C42×Dic61, C23×#14519684, C22×#16839608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17665);