Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1832 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator, socle | C23×C61 | C22×C4 |
| Fitting | C61×#376 | C2 |
| hypercenter | #376 | D61 |
| hypocenter | C61 | #1832 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
216 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,b^2=e,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^60,c^b=cg1244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29574139, #29574140, #29584087, … |
| maximal normal subgroup of | #29574139, #29574140, #29584087, … |
| maximal quotient of | #29573667, #29573671, #29573684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4630);