Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4×C8 | C2×D61 |
| commutator | C2×C61 | C82 |
| Fitting | C4×C16×C61 | C2 |
| socle | C22×C61 | C4×C8 |
| hypercenter | C4×C16 | D61 |
| hypocenter | C61 | #1311 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4×C8 ◁ C4×C16 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=bg,h^b=h^602000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29567342, #29567347, #29567680, … |
| maximal normal subgroup of | #29567342, #29567347, #29567680, … |
| maximal quotient of | #29566627, #29566628, #29566840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2426);