Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#16839516 |
| Sylow | C61 ⋊ C2×#336 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D61 |
| commutator | C2×C61 | C2×C4×C8 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C23×C8×C61 | C2 |
| socle | C24×C61 | C2×C4 |
| hypercenter | C23×C8 | D61 |
| hypocenter | C61 | C2×#336 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23×C4 ◁ C23×C8 | |
528 conjugacy classes of subgroups.
2000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566963, #29566965, #336×Dic61, … |
| maximal normal subgroup of | #29566963, #29566965, #336×Dic61, … |
| maximal quotient of | C2×#21443646, #29569395, #29569396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4200);