Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C337 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #13062438 |
| commutator, hypocenter | C337 | C32 |
| Fitting | C8×C337 | C4 |
| socle, prime radical | C2×C337 | C16 |
| cosocle | #19129160 | C2 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^148,f^b=f^336704 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#24925009, #36342236, #36342237, … |
| maximal normal subgroup of | C2×#24925009, #36342236, #36342237, … |
| maximal quotient of | #36342144, C2×#24925009 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 196);