Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C101 ⋊ #336 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C2×D101 |
| commutator | C2×C101 | C4×C8 |
| Fitting | C22×C8×C101 | C2 |
| socle | C23×C101 | C2×C4 |
| hypercenter | C22×C8 | D101 |
| hypocenter | C101 | #336 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=d,b^2=e,d^2=f,b^a=bc,g^b=g^1001640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×D101, C2×#20264931, #27170824, … |
| maximal normal subgroup of | #336×D101, C2×#20264931, #27170824, … |
| maximal quotient of | #27168959, #27168960, #27168962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 303);