Finite Group DatabasebetaFinite Group Databasebeta| order | 592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C37 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D37 |
| commutator, cosocle | C4×C37 | C22 |
| Frattini | C4 | C2×D37 |
| Fitting, prime radical | D4×C37 | C2 |
| socle | C2×C37 | D4 |
| hypercenter | D4 | D37 |
| hypocenter | C37 | SD16 |
| LCS | G ▷ C4×C37 ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^4,37|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^36,c^b=cd97 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D37, C2×#10596940, #11924555, … |
| maximal normal subgroup of | SD16×D37, C2×#10596940, #11924555, … |
| maximal quotient of | #11924457, #11924459, #11924467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(592, 16);