Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C47 · Schur multiplier (H2) = C26 |
| direct product | C47×#2888 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | C22×C22⋊C4 |
| commutator | C22 | C23×C4×C47 |
| Frattini, cosocle | C2×C4 | C24×C47 |
| prime radical | C2×H(5,𝔽2)×C47 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C2×#41×C47 ◁ G | |
756 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 340 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1927 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#13097, C47×#13099, C47×#21778, … |
| maximal normal subgroup of | C47×#13097, C47×#13099, C47×#21778, … |
| maximal quotient of | C47×#17350, C47×#17353, C47×#17367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 1620);