Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C47 · Schur multiplier (H2) = C29 |
| direct product | D4×#41×C47 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C47 |
| socle | C22×C47 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ G | |
1648 conjugacy classes of subgroups.
2350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#8436, C47×#17507, C47×#17511, … |
| maximal normal subgroup of | C47×#8436, C47×#17507, C47×#17511, … |
| maximal quotient of | C22⋊C4×#41×C47, C4⋊C4×#41×C47, D4×#117×C47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2200);