Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#10596925 |
| derived, Sylow | C37 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D37 |
| commutator, hypocenter | C37 | C22×C16 |
| Frattini | C8 | C22×D37 |
| Fitting | C22×C8×C37 | C2 |
| socle, prime radical | C23×C37 | C8 |
| cosocle | C8×C37 | C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C22×C8 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #17992673, #17992674, #17992685, … |
| maximal normal subgroup of | #17992673, #17992674, #17992685, … |
| maximal quotient of | C2×C4×#10596925, C2×C22⋊#10596925, C2×C4⋊#10596925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 961);