Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| isoclinism | isoclinic class of D101 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×D101 |
| Fitting | C22×C8×C101 ⋊ C2 |
| derived, Sylow | C101 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D101 |
| commutator, hypocenter | C101 | C23×C8 |
| Frattini | C4 | C23×D101 |
| Fitting | C22×C8×C101 | C2 |
| socle | C23×C101 | C2×C4 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
1664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×D101, #27170827, #340×D101, … |
| maximal normal subgroup of | #336×D101, #27170827, #340×D101, … |
| maximal quotient of | C2×C4×C8×D101, C22×C8×Dic101, C2×C22⋊C8×D101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1305);