Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D296 |
| Fitting | C22×C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ C22×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D148 |
| commutator, cosocle | C4×C37 | C24 |
| Frattini | C4 | C23×D37 |
| Fitting | C22×C8×C37 | C2 |
| socle | C23×C37 | D4 |
| hypercenter | C22×C8 | D37 |
| hypocenter | C37 | C22×D8 |
| LCS | G ▷ C4×C37 ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #17994943, #17994945, #17995460, … |
| maximal normal subgroup of | #17994943, #17994945, #17995460, … |
| maximal quotient of | C22×#11924458, C22×#11924470, C2×C4×D296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1319);