Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C5×C3⋊D15 |
| Fitting, socle | C22×C32×C52 ⋊ C2 |
| derived | C32×C5 ⋊ C23×C5 |
| Hall | C32×C52 ⋊ C23 |
| Sylow | C52 ⋊ C22×C3⋊D3 |
| Sylow | C32 ⋊ C22×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | C3⋊D15 |
| commutator, cosocle, hypocenter | C32×C5 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C52 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C22×C5 | |
444 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#11744719, C22×C5×D5×C3⋊D3, C22×D5×C3⋊D15, … |
| maximal normal subgroup of | C22×#11744719, C22×C5×D5×C3⋊D3, C22×D5×C3⋊D15, … |
| maximal quotient of | C2×C5×#67184 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 742);