Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C101 · Schur multiplier (H2) = C22×C4 |
| direct product | #493×C101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C101 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C42×C101 ◁ G | |
162 conjugacy classes of subgroups.
2222 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×#1357, C101×#1361, C101×#1408, … |
| maximal normal subgroup of | C101×#1357, C101×#1361, C101×#1408, … |
| maximal quotient of | C101×#1706, C101×#1709, C101×#1712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 174);