Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×#14519683 |
| derived, Sylow | C61 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D61 |
| commutator, hypocenter | C61 | C22×C32 |
| Frattini | C16 | C22×D61 |
| Fitting | C22×C16×C61 | C2 |
| socle | C23×C61 | C16 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
2048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29567699, #29567700, #29567711, … |
| maximal normal subgroup of | #29567699, #29567700, #29567711, … |
| maximal quotient of | C2×C4×#14519683, C2×C22⋊#14519683, C2×C4⋊#14519683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6799);