Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D37⋊C16 |
| derived, Sylow | C37 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #3866 |
| commutator, hypocenter | C37 | C2×C16 |
| Frattini | C4 | C2×#3866 |
| Fitting | C8×C37 | C4 |
| socle | C2×C37 | C2×C8 |
| prime radical | C2×D37 | C8 |
| cosocle | #64436 | C22 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^5,37|a^2=c,c^2=d,d^2=e,f^a=f^31,f^b=f^36,f^c=f^36104 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#3866, #14558420, #14558445, … |
| maximal normal subgroup of | C16×#3866, #14558420, #14558445, … |
| maximal quotient of | #14558419, #14558428, #14558454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 219);