Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C61 ⋊ #1780 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator, socle | C23×C61 | C22×C4 |
| Fitting | C22×Q8×C61 | C4 |
| hypercenter | C22×Q8 | #6923 |
| hypocenter | C61 | #1780 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
612 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^11,c^b=cg,h^b=h^60,h^c=h^60,h^f=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | #30594727, #30598557, #30598562, … |
| maximal normal subgroup of | #30594727, #30598557, #30598562, … |
| maximal quotient of | #30598138, #30598141, #30598144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20335);