Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C101 ⋊ #393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D101 |
| commutator, socle | C23×C101 | C23 |
| Fitting | C2×C22⋊C4×C101 | C2 |
| hypercenter | C2×C22⋊C4 | D101 |
| hypocenter | C101 | #393 |
| LCS | G ▷ C23×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,101|a^2=d,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^1001022 conjugacy classes — view the full character table.
| maximal subgroup of | #27169152, #27169154, #27170084, … |
| maximal normal subgroup of | #27169152, #27169154, #27170084, … |
| maximal quotient of | #27169375, #27169377, #27169388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 461);