Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C101 · Schur multiplier (H2) = C2 |
| direct product | #359×C101 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C101 | D8 |
| commutator | C8 | C2×C4×C101 |
| Frattini, cosocle | C2×C8 | C22×C101 |
| socle | C2×C101 | #102 |
| prime radical | #135×C101 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C101 ◁ C2×C4×C101 ◁ C2×C8×C101 ◁ G | |
56 conjugacy classes of subgroups.
2222 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#359×C101, C101×#2143, C101×#2178, … |
| maximal normal subgroup of | C2×#359×C101, C101×#2143, C101×#2178, … |
| maximal quotient of | C101×#1331, C101×#1332, C101×#1349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 40);