Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#16840628 |
| Sylow | C61 ⋊ C2×#336 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×#6923 |
| commutator | C2×C61 | C2×C4×C8 |
| Frattini | C23 | C22×#6923 |
| Fitting | C23×C4×C61 | C4 |
| socle | C24×C61 | C2×C4 |
| hypercenter | C23×C4 | #6923 |
| hypocenter | C61 | C2×#336 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
528 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #30593922, #30593944, #30593955, … |
| maximal normal subgroup of | #30593922, #30593944, #30593955, … |
| maximal quotient of | C2×#21460641, #30595984, #30595990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20170);