Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #95×C101 ⋊ C2 |
| Sylow | C101 ⋊ #393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D101 |
| commutator, socle | C23×C101 | C23 |
| Fitting | #95×C101 | C2 |
| hypercenter | #95 | D101 |
| hypocenter | C101 | #393 |
| LCS | G ▷ C23×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ #95 | |
202 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 61 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^100,g^c=g^1001022 conjugacy classes — view the full character table.
| maximal subgroup of | #27170085, #27170090, #27170113, … |
| maximal normal subgroup of | #27170085, #27170090, #27170113, … |
| maximal quotient of | #27169376, #27169378, #27169387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 462);