Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic37 |
| derived, Sylow | C37 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D37 |
| commutator, hypocenter | C37 | C24×C4 |
| Frattini | C2 | C24×D37 |
| Fitting, socle, prime radical | C25×C37 | C2 |
| cosocle | C2×C37 | C25 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C25 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #17992818, C22×#11924443, C2×C22⋊C4×Dic37, … |
| maximal normal subgroup of | #17992818, C22×#11924443, C2×C22⋊C4×Dic37, … |
| maximal quotient of | C23×C4×Dic37, C23×C22⋊Dic37, C23×C4⋊Dic37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1368);