Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C42 | C2×D61 |
| commutator | C2×C61 | C82 |
| Fitting | C2×C4×C8×C61 | C2 |
| socle | C23×C61 | C42 |
| hypercenter | C2×C4×C8 | D61 |
| hypocenter | C61 | #1273 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^b=h^602000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566785, #29566786, #29566798, … |
| maximal normal subgroup of | #29566785, #29566786, #29566798, … |
| maximal quotient of | #29566539, #29566540, #29566541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2337);