Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#13108049 |
| derived, Sylow | C101 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D101 |
| commutator, hypocenter | C101 | C22×C16 |
| Frattini | C8 | C22×D101 |
| Fitting | C22×C8×C101 | C2 |
| socle | C23×C101 | C8 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C22×C8 | |
98 conjugacy classes of subgroups.
1664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27169209, #27169210, #27169221, … |
| maximal normal subgroup of | #27169209, #27169210, #27169221, … |
| maximal quotient of | C2×C4×#13108049, C2×C22⋊#13108049, C2×C4⋊#13108049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 961);