Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C47 · Schur multiplier (H2) = C4 |
| direct product | C47×#1307 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | #95 |
| commutator | C23 | C42×C47 |
| Frattini, cosocle | C2×C42 | C22×C47 |
| prime radical | C23×C47 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G | |
130 conjugacy classes of subgroups.
1222 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#7415, C47×#7441, C2×C47×#1307, … |
| maximal normal subgroup of | C47×#7415, C47×#7441, C2×C47×#1307, … |
| maximal quotient of | C47×#7033, C47×#7034, C47×#7040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 39);