Finite Group DatabasebetaFinite Group Databasebeta| order | 4618 |
| automorphism | Aut(G) order 5329172 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2309 |
| unambiguous semidirect product | C2309⋊C2 |
| Fitting, socle, derived, Sylow | C2309 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C2309 | C2 |
| LCS | G ▷ C2309 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 2309 |
| transitive degree | μt(G) = 2309 |
Polycyclic presentation:
2,2309|b^a=b^23081156 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2309, D6927, C5×D2309, … |
| maximal normal subgroup of | C3×D2309, C5×D2309, C7×D2309 |
| maximal quotient of | C3×D2309, D6927, C5×D2309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4618, 1);