Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| isoclinism | isoclinic class of D101 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic101 |
| derived, Sylow | C101 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D101 |
| commutator, hypocenter | C101 | C24×C4 |
| Frattini | C2 | C24×D101 |
| Fitting, socle | C25×C101 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C25 | |
1362 conjugacy classes of subgroups.
1664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1368);