Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C101 · Schur multiplier (H2) = C22 |
| direct product | #343×C101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C22⋊C4 |
| commutator | C22 | C42×C101 |
| Frattini, cosocle | C22×C4 | C22×C101 |
| prime radical | C23×C101 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C22×C4×C101 ◁ G | |
98 conjugacy classes of subgroups.
2222 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×#1345, C101×#1346, C101×#1353, … |
| maximal normal subgroup of | C101×#1345, C101×#1346, C101×#1353, … |
| maximal quotient of | C101×#1280, C101×#1283, C101×#1285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 24);