Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C32×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1423 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16840688 |
| commutator | C16×C61 | C2×C4 |
| Frattini | C16 | C2×#6923 |
| Fitting | C32×C61 | C4 |
| socle | C2×C61 | #366 |
| hypercenter | C32 | #6923 |
| hypocenter | C61 | #1423 |
| LCS | G ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,b^2=ce,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^11,h^d=h^60518 conjugacy classes — view the full character table.
| maximal subgroup of | #30595297, #30595298, #30595309, … |
| maximal normal subgroup of | #30595297, #30595298, #30595309, … |
| maximal quotient of | #30595068, #30595069, #30595100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19671);