Finite Group DatabasebetaFinite Group Databasebeta| order | 4904 |
| automorphism | Aut(G) order 3001248 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1226 |
| unambiguous semidirect product | C613⋊Q8 |
| Sylow | C613 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D613 |
| commutator, socle | C2×C613 | C22 |
| Fitting | C4×C613 | C2 |
| hypercenter | C4 | D613 |
| hypocenter | C613 | Q8 |
| LCS | G ▷ C2×C613 ▷ C613 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,613|a^2=c,b^2=c,b^a=bc,d^b=d^6121229 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3678, Dic6130, Dic8582, … |
| maximal quotient of | Dic3678, Dic6130, Dic8582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4904, 11);