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 | C2×C4 | C22×D101 |
| commutator, socle | C22×C101 | C22×C4 |
| Fitting | C2×#41×C101 | C2 |
| hypercenter | C2×#41 | D101 |
| hypocenter | C101 | #408 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=e,e^2=f,b^a=bd,g^a=g^100,c^b=cf1028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27169252, #27169254, #27169260, … |
| maximal normal subgroup of | #27169252, #27169254, #27169260, … |
| maximal quotient of | #27169480, #27169484, #27169488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 516);