Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C47 · Schur multiplier (H2) = C28 |
| direct product | C2×C47×#562 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C47 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C47 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C47 ◁ G | |
1152 conjugacy classes of subgroups.
1786 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#8508, C2×C47×#1656, C2×C47×#1661, … |
| maximal normal subgroup of | C47×#8508, C2×C47×#1656, C2×C47×#1661, … |
| maximal quotient of | C2×C47×#2376, C2×C47×#2377, C2×C47×#2378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2259);