Finite Group DatabasebetaFinite Group Databasebeta| order | 5392 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C337 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #14582115 |
| commutator, hypocenter | C337 | C16 |
| Fitting, socle | C2×C337 | C8 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,337|a^2=b,b^2=c,c^2=d,e^a=e^85,e^b=e^148,e^c=e^336100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5392, 52);