Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#13108051 |
| Fitting | C2×C42×C101 ⋊ C2 |
| Sylow | C101 ⋊ C4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D101 |
| commutator | C2×C101 | C2×C42 |
| Frattini | C23 | C22×D101 |
| Fitting | C2×C42×C101 | C2 |
| socle | C23×C101 | C23 |
| hypercenter | C2×C42 | D101 |
| hypocenter | C101 | C4×C22⋊C4 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27170902, C8×#13108051, #27170907, … |
| maximal normal subgroup of | #27170902, C8×#13108051, #27170907, … |
| maximal quotient of | C4×#15692162, #27169353, #27169356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 398);