Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C101 ⋊ #435 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#87938 |
| commutator, socle | C22×C101 | C22×C4 |
| Fitting | C4⋊C4×C101 | C4 |
| hypercenter | C4⋊C4 | #87938 |
| hypocenter | C101 | #435 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^10,g^b=g^100,g^c=g^10,g^e=g^100278 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20266207, D101⋊#435, #27187848, … |
| maximal normal subgroup of | C2×#20266207, D101⋊#435, #27187848, … |
| maximal quotient of | #27186732, #27186736, #27186740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1579);