Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×#41×C61 ⋊ C4 |
| Sylow | C61 ⋊ #2297 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Frattini | C22 | C23×#6923 |
| Fitting | C2×#41×C61 | C4 |
| hypercenter | C2×#41 | #6923 |
| hypocenter | C61 | #2297 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
936 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=eg,d^2=f,b^a=be,c^a=cf,h^a=h^50,h^b=h^11,h^g=h^60356 conjugacy classes — view the full character table.
| maximal subgroup of | #30602458, #30602459, #30602474, … |
| maximal normal subgroup of | #30602458, #30602459, #30602474, … |
| maximal quotient of | #30608619, #30608629, C4×#16840710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20971);