Finite Group DatabasebetaFinite Group Databasebeta| order | 6568 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C821 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D821 |
| commutator, hypocenter | C821 | C8 |
| Fitting | C4×C821 | C2 |
| socle | C2×C821 | C4 |
| LCS | G ▷ C821 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,821|a^2=b,b^2=c,d^a=d^8201648 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D821, C2×#20267100, #27190132, … |
| maximal normal subgroup of | C8×D821, C2×#20267100, #27190132, … |
| maximal quotient of | #27190124, C2×#20267100 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6568, 6);