Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C509 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #14523266 |
| commutator, hypocenter | C509 | C4×C16 |
| Frattini | C2×C4 | C2×#14523266 |
| Fitting | C2×C8×C509 | C4 |
| socle, prime radical | C22×C509 | C2×C8 |
| cosocle | C2×#16861325 | C22 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32576 |
Polycyclic presentation:
2^6,509|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^301,g^b=g^508,g^c=g^5082096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1435);