Finite Group DatabasebetaFinite Group Databasebeta| order | 5392 |
| automorphism | Aut(G) order 3623424 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1348 |
| Sylow | C337 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D1348 |
| commutator | C4×C337 | C22 |
| Frattini | C4 | C2×D337 |
| Fitting | C8×C337 | C2 |
| socle | C2×C337 | D4 |
| hypercenter | C8 | D337 |
| hypocenter | C337 | Q16 |
| LCS | G ▷ C4×C337 ▷ C2×C337 ▷ C337 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,337|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^336,c^b=cd,e^b=e^3361351 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic4044, Dic6740, Dic9436, … |
| maximal quotient of | Dic4044, Dic6740, Dic9436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5392, 31);