Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×M16×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator | C2×C61 | C22×C42 |
| Fitting | C4×M16×C61 | C2 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C4×M16 | D61 |
| hypocenter | C61 | #2875 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=f,e^2=g,b^a=bg,h^a=h^60,d^c=dg,h^d=h^601268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29576823, #29576827, #29576830, … |
| maximal normal subgroup of | #29576823, #29576827, #29576830, … |
| maximal quotient of | #29645607, #29645628, #29645687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 12939);