Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #11744719 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#11744719 |
| Fitting, socle | C2×C32×C52 ⋊ C22 |
| derived, Hall | C32×C52 ⋊ C23 |
| Sylow | C52 ⋊ C22×C3⋊D3 |
| Sylow | C32 ⋊ C2×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11744719 |
| commutator, cosocle, hypocenter | C32×C52 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C22 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
444 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #72229316, #72229341, #72229351, … |
| maximal normal subgroup of | #72229316, #72229341, #72229351, … |
| maximal quotient of | #72229351, C2×#14268268, C22×#11744719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 730);