Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C101 · Schur multiplier (H2) = C23 |
| direct product | #342×C101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C22⋊C4 |
| commutator | C22 | C42×C101 |
| Frattini, cosocle | C24 | C22×C101 |
| prime radical | C24×C101 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C24×C101 ◁ G | |
142 conjugacy classes of subgroups.
2222 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×#1343, C101×#1344, C101×#1351, … |
| maximal normal subgroup of | C101×#1343, C101×#1344, C101×#1351, … |
| maximal quotient of | C101×#1280, C101×#1282, C101×#1284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 23);