Finite Group DatabasebetaFinite Group Databasebeta| order | 4606 |
| automorphism | Aut(G) order 4449396 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2303 |
| unambiguous semidirect product | C47⋊D49 |
| unambiguous semidirect product | C49⋊D47 |
| Fitting, derived, Hall | C47×C49 ⋊ C2 |
| Sylow | C49 ⋊ D47 |
| Sylow | C47 ⋊ D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C47×C49 | C2 |
| Frattini | C7 | D329 |
| socle | C7×C47 | D7 |
| LCS | G ▷ C47×C49 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 2303 |
Polycyclic presentation:
2,7,47,7|b^7=d^6,b^a=b^6d,c^a=c^46,d^a=d^61153 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47⋊(D49⋊C3), C3×D2303, D6909, … |
| maximal normal subgroup of | C47⋊(D49⋊C3), C3×D2303, C5×D2303 |
| maximal quotient of | C3×D2303, D6909, C5×D2303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4606, 4);