Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C61×#391 ⋊ C2 |
| Sylow | C61 ⋊ #2297 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator | C22×C61 | C23×C4 |
| Fitting | C61×#391 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | #391 | D61 |
| hypocenter | C61 | #2297 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #391 | |
936 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=eg,d^2=f,b^a=be,c^a=cf,h^b=h^60,h^c=h^60,h^d=h^60896 conjugacy classes — view the full character table.
| maximal subgroup of | #29567964, #29568024, #29568110, … |
| maximal normal subgroup of | #29567964, #29568024, #29568110, … |
| maximal quotient of | #29601127, #29601152, #29601159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6999);