Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C61 ⋊ #1444 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D61 |
| commutator | C23×C61 | C22×C4 |
| Fitting | C22×C4⋊C4×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C22×C4⋊C4 | D61 |
| hypocenter | C61 | #1444 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
608 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=d,c^2=e,b^a=bd,c^a=ce,c^b=cf,h^c=h^601244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29574058, #29574059, #29574072, … |
| maximal normal subgroup of | #29574058, #29574059, #29574072, … |
| maximal quotient of | #29567939, #29567940, #29588615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2773);