Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | #433×D47 |
| Fitting | C47×#433 ⋊ C2 |
| Sylow | C47 ⋊ C2×#433 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D47 |
| commutator, socle | C22×C47 | C23×C4 |
| Fitting | C47×#433 | C2 |
| hypercenter | #433 | D47 |
| hypocenter | C47 | C2×#433 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
412 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#433×D47, D47×#2921, D47×#2922, … |
| maximal normal subgroup of | C2×#433×D47, D47×#2921, D47×#2922, … |
| maximal quotient of | D47×#1746, D47×#1750, D47×#1768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13132);