Finite Group DatabasebetaFinite Group Databasebeta| order | 5392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic337 |
| Sylow | C337 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D337 |
| commutator | C2×C337 | C2×C4 |
| Fitting | C2×C4×C337 | C2 |
| socle | C22×C337 | C22 |
| hypercenter | C2×C4 | D337 |
| hypocenter | C337 | C4⋊C4 |
| LCS | G ▷ C2×C337 ▷ C337 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,337|a^2=d,b^2=c,b^a=bc,e^a=e^3361354 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5392, 20);