Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×#16839481 |
| derived, Sylow | C61 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D61 |
| commutator, hypocenter | C61 | C2×C64 |
| Frattini | C32 | C2×D61 |
| Fitting | C2×C32×C61 | C2 |
| socle | C22×C61 | C32 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C32 | |
40 conjugacy classes of subgroups.
2048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×Dic61, C4×#16839481, #29567817, … |
| maximal normal subgroup of | C64×Dic61, C4×#16839481, #29567817, … |
| maximal quotient of | C4×#16839481, C22⋊#16839481, C4⋊#16839481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2719);