Finite Group DatabasebetaFinite Group Databasebeta| order | 33344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C521 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #16861969 |
| commutator, hypocenter | C521 | C2×C32 |
| Frattini | C4 | C2×#16861969 |
| Fitting | C8×C521 | C8 |
| socle | C2×C521 | C2×C16 |
| prime radical | C2×D521 | C16 |
| cosocle | #22552367 | C22 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C8 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16672 |
Polycyclic presentation:
2^6,521|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^315,g^b=g^520,g^c=g^235,g^d=g^520584 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33344, 1656);