Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C101 ⋊ #408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#87938 |
| commutator, socle | C22×C101 | C22×C4 |
| Fitting | C2×D4×C101 | C4 |
| hypercenter | C2×D4 | #87938 |
| hypocenter | C101 | #408 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=e,e^2=f,b^a=bd,g^a=g^10,c^b=cf,g^c=g^100,g^e=g^100278 conjugacy classes — view the full character table.
| maximal subgroup of | #27186231, #27186980, #27187089, … |
| maximal normal subgroup of | #27186231, #27186980, #27187089, … |
| maximal quotient of | #27186398, #27186402, #27186405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1523);