Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C101 · Schur multiplier (H2) = C23 |
| direct product | #442×C101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C2×D4 |
| commutator | C4 | C22×C4×C101 |
| Frattini, cosocle | C2×C4 | C23×C101 |
| prime radical | C2×D8×C101 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C42×C101 ◁ G | |
132 conjugacy classes of subgroups.
2222 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×AGL(1,ℤ/16), C2×#442×C101, C101×#2943, … |
| maximal normal subgroup of | C101×AGL(1,ℤ/16), C2×#442×C101, C101×#2943, … |
| maximal quotient of | C101×#1580, C101×#1586, C101×#1594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 123);