Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×D37 |
| Fitting | C4⋊Q8×C37 ⋊ C2 |
| Sylow | C37 ⋊ C2×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Fitting | C4⋊Q8×C37 | C2 |
| prime radical | C22×D37 | C23 |
| hypercenter | C4⋊Q8 | D37 |
| hypocenter | C37 | C2×C4⋊Q8 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #332×D37, #333×D37, #17993266, … |
| maximal normal subgroup of | #332×D37, #333×D37, #17993266, … |
| maximal quotient of | #384×D37, #389×D37, #391×D37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1090);