Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C101 ⋊ #385 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D101 |
| commutator | C22×C101 | C22×C4 |
| Fitting | C23×C4×C101 | C2 |
| socle | C23×C101 | C23 |
| hypercenter | C23×C4 | D101 |
| hypocenter | C101 | #385 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 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=f,b^2=f,b^a=bd,c^a=ce,g^a=g^1001628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27171411, #27171412, #27172381, … |
| maximal normal subgroup of | #27171411, #27171412, #27172381, … |
| maximal quotient of | #27169355, #27169365, #27169375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 422);