Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | C4×#14519687 |
| Sylow | C61 ⋊ C4×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×D61 |
| commutator | C2×C61 | C43 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C2×C4×C8×C61 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C4×C8 | D61 |
| hypocenter | C61 | C4×#97 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
360 conjugacy classes of subgroups.
2000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566870, C8×#14519687, #29569365, … |
| maximal normal subgroup of | #29566870, C8×#14519687, #29569365, … |
| maximal quotient of | C4×#16839483, C4×#16839484, C8×#14519687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4194);