Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#1043 |
| Fitting, socle, Hall | C32×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #1043 |
| commutator, hypocenter | C52 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52 | C4 |
| prime radical | C32×C5⋊D5 | C2 |
| cosocle | C5⋊D5 | C2×C32 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C32 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 225 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#6053, C3×C3⋊#6053, C3⋊(C3⋊#6053), … |
| maximal normal subgroup of | C32×#6053, C3×C3⋊#6053, C3⋊(C3⋊#6053), … |
| maximal quotient of | C32×#6033, C2×C32×#1043, C3×#16839081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 105);