Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#14519747 |
| Fitting | C4×C22⋊C4×C61 ⋊ C2 |
| Sylow | C61 ⋊ C4×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D61 |
| commutator | C22×C61 | C23×C4 |
| Frattini | C23 | C23×D61 |
| Fitting | C4×C22⋊C4×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C4×C22⋊C4 | D61 |
| hypocenter | C61 | C4×#120 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
1224 conjugacy classes of subgroups.
1256 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29574697, #29574707, #29685507, … |
| maximal normal subgroup of | #29574697, #29574707, #29685507, … |
| maximal quotient of | C4×#16839640, C4×#16839639, C4×#16839637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 7014);