Finite Group DatabasebetaFinite Group Databasebeta| order | 3020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic151⋊C5 |
| unambiguous semidirect product | (C151⋊C5)⋊C4 |
| derived, Sylow | C151 ⋊ C4×C5 |
| Hall | C151⋊C5 ⋊ C4 |
| Hall | Dic151 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D151⋊C5 |
| commutator, hypocenter | C151 | C4×C5 |
| Fitting, socle, cosocle | C2×C151 | C2×C5 |
| prime radical | C2×C151⋊C5 | C2 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 155 |
| transitive degree | μt(G) = 604 |
Polycyclic presentation:
2,5,151,2|a^2=d,c^a=c^150,c^b=c^5950 conjugacy classes — view the full character table.
| maximal subgroup of | #16836851⋊C4, C5×Dic151⋊C5, (C151⋊C5)⋊Dic5, … |
| maximal normal subgroup of | #16836851⋊C4, C5×Dic151⋊C5, C7×Dic151⋊C5, … |
| maximal quotient of | #16836849⋊C4, C5×Dic151⋊C5, (C151⋊C5)⋊Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3020, 2);