Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C101 ⋊ #322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C2×D101 |
| commutator | C2×C101 | C4×C8 |
| Fitting | C4×C8×C101 | C2 |
| socle | C22×C101 | C42 |
| hypercenter | C4×C8 | D101 |
| hypocenter | C101 | #322 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^a=g^1001640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #322×D101, C2×#20264899, C8×#13108057, … |
| maximal normal subgroup of | #322×D101, C2×#20264899, C8×#13108057, … |
| maximal quotient of | #27168959, #27169051, #27169053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 271);