Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×#3866 |
| unambiguous semidirect product | D37⋊(C2×C42) |
| Fitting | C22×C4×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #3866 |
| commutator, hypocenter | C37 | C22×C42 |
| Frattini | C2 | C23×#3866 |
| Fitting | C22×C4×C37 | C4 |
| socle | C23×C37 | C2×C4 |
| prime radical | C23×D37 | C22 |
| cosocle | C2×D37 | C24 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C22×C4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #95×#3866, C4×(C2×#3866)⋊C4, #18009771, … |
| maximal normal subgroup of | #95×#3866, C4×(C2×#3866)⋊C4, #18009771, … |
| maximal quotient of | C2×C42×#3866, C22×(C2×#3866)⋊C4, C2×#14558469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1609);