Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#11758190 |
| Fitting | C23×C8×C61 ⋊ C2 |
| Sylow | C61 ⋊ C23×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D244 |
| commutator | C4×C61 | C25 |
| Frattini | C4 | C24×D61 |
| Fitting | C23×C8×C61 | C2 |
| socle | C24×C61 | D4 |
| hypercenter | C23×C8 | D61 |
| hypocenter | C61 | C23×SD16 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1720 conjugacy classes of subgroups.
1976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29586816, #29586820, #29586843, … |
| maximal normal subgroup of | #29586816, #29586820, #29586843, … |
| maximal quotient of | C23×#14519699, C23×#14519702, C23×#14519709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19230);