Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1746 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator | C22×C61 | C2×C42 |
| Fitting | C2×C4×C8×C61 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C4×C8 | D61 |
| hypocenter | C61 | #1746 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×C8 | |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,c^b=cg,h^b=h^601976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566858, #29566860, #29570468, … |
| maximal normal subgroup of | #29566858, #29566860, #29570468, … |
| maximal quotient of | #29570439, #29570442, #29570445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4261);