Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C101 · Schur multiplier (H2) = C23 |
| direct product | #340×C101 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C101 | D4 |
| commutator | C4 | C42×C101 |
| Frattini, cosocle | C22×C4 | C22×C101 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C101 ◁ C22×C4×C101 ◁ G | |
114 conjugacy classes of subgroups.
2828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×#1347, C101×#1348, C2×#340×C101, … |
| maximal normal subgroup of | C101×#1347, C101×#1348, C2×#340×C101, … |
| maximal quotient of | C101×#1277, C101×#1279, C101×#1286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 21);