Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C2×D61 |
| commutator, socle | C2×C61 | C22×C16 |
| Frattini | C16 | C22×D61 |
| Fitting | C2×C32×C61 | C2 |
| hypercenter | C2×C32 | D61 |
| hypocenter | C61 | #2258 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C32 ◁ C2×C32 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,d^2=e,e^2=f,f^2=g,c^b=cg,h^c=h^602000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29567825, #29567827, #29600575, … |
| maximal normal subgroup of | #29567825, #29567827, #29600575, … |
| maximal quotient of | #29600191, #29600192, #29600208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6803);