Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C337 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14582115 |
| commutator, socle | C2×C337 | C2×C8 |
| Fitting, prime radical | C22×C337 | C8 |
| cosocle | #14582113 | C22 |
| hypercenter | C22 | #14582115 |
| hypocenter | C337 | M32 |
| LCS | G ▷ C2×C337 ▷ C337 | |
| UCS | C1 ◁ C2 ◁ C22 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^85,f^c=f^148,f^d=f^336188 conjugacy classes — view the full character table.
| maximal subgroup of | #36342403, #36342404, C2×#24925055, … |
| maximal normal subgroup of | #36342403, #36342404, C2×#24925055, … |
| maximal quotient of | #36342399, C22⋊#19129197, #36342408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 242);