Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C101 · Schur multiplier (H2) = C2 |
| direct product | Q8⋊C8×C101 |
| unambiguous semidirect product | Q8⋊(C8×C101) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C101 | D4 |
| commutator | C4 | C2×C8×C101 |
| Frattini, cosocle | C42 | C22×C101 |
| socle, prime radical | C22×C101 | C22⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C101 ◁ C42×C101 ◁ G | |
70 conjugacy classes of subgroups.
2828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×Q8⋊C8×C101, C101×#1476, C101×#1477, … |
| maximal normal subgroup of | C2×Q8⋊C8×C101, C101×#1476, C101×#1477, … |
| maximal quotient of | C101×#1271, C101×#1272, C101×#1279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 7);