Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C61 ⋊ C2 |
| Sylow | C61 ⋊ #508 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D8×D61 |
| commutator, cosocle | C8×C61 | C23 |
| Frattini | C8 | C22×D61 |
| Fitting | Q32×C61 | C2 |
| socle | C2×C61 | C2×D8 |
| hypercenter | Q32 | D61 |
| hypocenter | C61 | #508 |
| LCS | G ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^6,61|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^60,d^b=de,e^b=ef,g^b=g^60,g^c=g^60352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 982);