Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D61 |
| commutator, socle, prime radical, cosocle | C23×C61 | C23 |
| Fitting | C2×C4⋊C4×C61 | C2 |
| hypercenter | C2×C4⋊C4 | D61 |
| hypocenter | C61 | #398 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^6,61|a^2=e,b^2=d,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^60622 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 480);