Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C64×D61 |
| Fitting | C61×C64 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C64 | D61 |
| commutator, hypocenter | C61 | C2×C64 |
| Frattini | C32 | C2×D61 |
| Fitting | C61×C64 | C2 |
| socle | C2×C61 | C2×C32 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C64 | |
40 conjugacy classes of subgroups.
2048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×C128, #29567923, C2×C64×D61, … |
| maximal normal subgroup of | D61×C128, #29567923, C2×C64×D61, … |
| maximal quotient of | C64×Dic61, #29567821, #29567908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2718);