Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D8×D37 |
| Fitting | C2×D8×C37 ⋊ C2 |
| Sylow | C37 ⋊ C22×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D37 |
| commutator, cosocle | C4×C37 | C24 |
| Frattini | C4 | C23×D37 |
| Fitting | C2×D8×C37 | C2 |
| socle | C22×C37 | C2×D4 |
| hypercenter | C2×D8 | D37 |
| hypocenter | C37 | C22×D8 |
| LCS | G ▷ C4×C37 ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D8 | |
338 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 592 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #357×D37, #17996310, #361×D37, … |
| maximal normal subgroup of | #357×D37, #17996310, #361×D37, … |
| maximal quotient of | C2×#102×D37, C2×#107×D37, C4×D8×D37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1317);