Finite Group DatabasebetaFinite Group Databasebeta| order | 4620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D165 |
| unambiguous semidirect product | (C3×D7)⋊D55 |
| unambiguous semidirect product | (C5×D7)⋊D33 |
| unambiguous semidirect product | (C11×D7)⋊D15 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C11 | C22 |
| LCS | G ▷ C3×C5×C7×C11 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 1155 |
420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D495, AGL(1,𝔽7)×D165, C3×D7×D165, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D165, C3×D7×D165, D7×C3⋊(C5⋊AGL(1,𝔽11)), … |
| maximal quotient of | D7×D495, C3×D7×D165, D7×C3⋊D165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4620, 102);