Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#441 ⋊ C2 |
| Sylow | C61 ⋊ #3317 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#441 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #441 | D61 |
| hypocenter | C61 | #3317 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #441 | |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=eg,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^60,c^b=cg,d^b=de,h^b=h^60,f^c=fg,h^d=h^60689 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#3317, C2×#21457950, #30556783, … |
| maximal normal subgroup of | D61×#3317, C2×#21457950, #30556783, … |
| maximal quotient of | #29695543, #29696381, #29697093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 16641);