Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#391 ⋊ C2 |
| Sylow | C61 ⋊ #2378 |
| 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 | #2378 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #391 | |
464 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=e,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,h^c=h^60878 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2378, C2×#21448980, #29842626, … |
| maximal normal subgroup of | D61×#2378, C2×#21448980, #29842626, … |
| maximal quotient of | #29601632, #29601641, #29601643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 7671);