Finite Group DatabasebetaFinite Group Databasebeta| order | 1872 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D13×#638 |
| Fitting | C22×C32×C13 ⋊ C22 |
| Hall | C32×C13 ⋊ C2×D4 |
| Sylow | C13 ⋊ C2×#638 |
| Sylow | C32 ⋊ D4×D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C3⋊D3×D13 |
| commutator, socle, cosocle | C2×C32×C13 | C23 |
| Fitting | C22×C32×C13 | C22 |
| hypercenter | C22 | C3⋊D3×D13 |
| hypocenter | C32×C13 | C2×D4 |
| LCS | G ▷ C2×C32×C13 ▷ C32×C13 | |
| UCS | C1 ◁ C2 ◁ C22 | |
324 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 468 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1872, 875);