Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×Dic5 |
| derived | C5 ⋊ C32×C4×C5 |
| Hall | C32×C52 ⋊ C4 |
| Sylow | C52 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C5 | D5 |
| commutator, hypocenter | C5 | C32×C4×C5 |
| Frattini | C2 | C32×C5×D5 |
| Fitting, socle, prime radical | C2×C32×C52 | C2 |
| cosocle | C2×C5 | C2×C32×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C32×C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C5×#170, C32×#6032, C3×C5×C3⋊#170, … |
| maximal normal subgroup of | C32×C5×#170, C32×#6032, C3×C5×C3⋊#170, … |
| maximal quotient of | C32×C5×#168, C2×C32×C5×Dic5, C3×C5×Dic65⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 79);