Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #418×D61 |
| Fitting | C61×#418 ⋊ C2 |
| Sylow | C61 ⋊ C2×#418 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#418 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #418 | D61 |
| hypocenter | C61 | C2×#418 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #418 | |
1008 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1795, D61×#1883, #29681541, … |
| maximal normal subgroup of | D61×#1795, D61×#1883, #29681541, … |
| maximal quotient of | D61×#1478, D61×#1490, #29646451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13008);