Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C47 · Schur multiplier (H2) = C24 |
| direct product | C47×#3380 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C47 |
| prime radical | C2×D8×C47 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C4×Q8×C47 ◁ G | |
352 conjugacy classes of subgroups.
1645 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#12355, C47×#12359, C47×#12407, … |
| maximal normal subgroup of | C47×#12355, C47×#12359, C47×#12407, … |
| maximal quotient of | C47×#22519, C4⋊C4×D8×C47, C47×#22682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2112);