Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×D37⋊C8 |
| unambiguous semidirect product | D37⋊(C22×C8) |
| derived, Sylow | C37 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #3866 |
| commutator, hypocenter | C37 | C23×C8 |
| Frattini | C2 | C23×#3866 |
| Fitting | C22×C4×C37 | C4 |
| socle | C23×C37 | C2×C4 |
| prime radical | C23×D37 | C4 |
| cosocle | Dic37 | C24 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C22×C4 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#3866)⋊C8, #18010257, #18010263, … |
| maximal normal subgroup of | C2×(C2×#3866)⋊C8, #18010257, #18010263, … |
| maximal quotient of | C22×C4×#64438, C2×C4×D37⋊C8, C2×D37⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1620);