Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| isoclinism | isoclinic class of D101 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×Dic101 |
| derived, Sylow | C101 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D101 |
| commutator, hypocenter | C101 | C22×C42 |
| Frattini | C22 | C23×D101 |
| Fitting | C23×C4×C101 | C2 |
| socle | C24×C101 | C22 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C23×C4 | |
498 conjugacy classes of subgroups.
1664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #95×Dic101, C4×#15692162, #27169356, … |
| maximal normal subgroup of | #95×Dic101, C4×#15692162, #27169356, … |
| maximal quotient of | C2×C42×Dic101, C22×#15692162, C2×#20265023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 994);