Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16840725 |
| Fitting | C22×C8×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×#6923 |
| commutator | C2×C61 | C22×C42 |
| Frattini | C4 | C23×#6923 |
| Fitting | C22×C8×C61 | C4 |
| socle | C22×C61 | C2×C42 |
| hypercenter | C22×C8 | #6923 |
| hypocenter | C61 | C2×#405 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
592 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #30602292, #30602293, #30602316, … |
| maximal normal subgroup of | #30602292, #30602293, #30602316, … |
| maximal quotient of | C2×C8×#11758217, C8×D61⋊M16, C2×C8×#11758213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21068);