Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C47 · Schur multiplier (H2) = C22 |
| direct product | C2×C47×#330 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C47 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C47 |
| Frattini, cosocle | C42 | C23×C47 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G | |
232 conjugacy classes of subgroups.
1786 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C47×#330, C47×#8225, C47×#8227, … |
| maximal normal subgroup of | C4×C47×#330, C47×#8225, C47×#8227, … |
| maximal quotient of | C2×C47×#1271, C47×#7568, C47×#7627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 255);