Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C24 |
| direct product | #564×C101 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C101 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C101 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ G | |
172 conjugacy classes of subgroups.
1919 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×#1658, C101×#1663, C2×#564×C101, … |
| maximal normal subgroup of | C101×#1658, C101×#1663, C2×#564×C101, … |
| maximal quotient of | C101×#2382, C101×#2719, C101×#2726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 245);