Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C337 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #14582115 |
| commutator, hypocenter | C337 | C2×C32 |
| Frattini | C4 | C2×#14582115 |
| Fitting | C8×C337 | C8 |
| socle | C2×C337 | C2×C16 |
| prime radical | C2×D337 | C16 |
| cosocle | #19129188 | C22 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C8 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10784 |
Polycyclic presentation:
2^6,337|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^85,g^b=g^336,g^c=g^148,g^d=g^336400 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1656);