Finite Group DatabasebetaFinite Group Databasebeta| order | 592 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D37⋊C8 |
| derived, Sylow | C37 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #3866 |
| commutator, hypocenter | C37 | C2×C8 |
| Frattini | C2 | C2×#3866 |
| Fitting | C4×C37 | C4 |
| socle | C2×C37 | C2×C4 |
| prime radical | C2×D37 | C4 |
| cosocle | Dic37 | C22 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^4,37|a^2=c,b^2=d,c^2=d,e^a=e^31,e^c=e^3652 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#3866, #11924590, #11924598, … |
| maximal normal subgroup of | C8×#3866, #11924590, #11924598, … |
| maximal quotient of | C4×#64438, #11924593, #11924603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(592, 28);