Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C101 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#87938 |
| commutator | C2×C101 | C2×C42 |
| Fitting | C22⋊C4×C101 | C4 |
| socle | C22×C101 | C22×C4 |
| hypercenter | C22⋊C4 | #87938 |
| hypocenter | C101 | #405 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=d,b^2=e,d^2=f,g^a=g^10,c^b=cf,g^d=g^100290 conjugacy classes — view the full character table.
| maximal subgroup of | #27186890, C2×#20266141, #27187692, … |
| maximal normal subgroup of | #27186890, C2×#20266141, #27187692, … |
| maximal quotient of | #27186333, #27186337, #27186343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1513);