Finite Group DatabasebetaFinite Group Databasebeta| order | 592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic37 |
| Sylow | C37 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D37 |
| commutator | C2×C37 | C2×C4 |
| Fitting | C2×C4×C37 | C2 |
| socle, prime radical, cosocle | C22×C37 | C22 |
| hypercenter | C2×C4 | D37 |
| hypocenter | C37 | C4⋊C4 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^4,37|a^2=c,b^2=d,b^a=bd,e^a=e^36154 conjugacy classes — view the full character table.
| maximal subgroup of | #11924457, #11924458, #11924460, … |
| maximal normal subgroup of | #11924457, #11924458, #11924460, … |
| maximal quotient of | #11924443, C4⋊#64436, #11924468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(592, 13);