Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of ((C5⋊D5)⋊C3)⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | ((C5⋊D5)⋊C3)⋊D3 |
| Fitting, socle | C3×C52 ⋊ C2×D3 |
| derived, Hall | C3×C52⋊C3 ⋊ C22 |
| Sylow | C52 ⋊ C2×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C52⋊C3 | C22 |
| Fitting, socle | C3×C52 | C2×D3 |
| LCS | G ▷ C3×C52⋊C3 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
Polycyclic presentation:
2^2,3^2,5^2|c^a=c^2,d^a=d^2,e^a=e^2f^3,f^a=e^4f^3,e^b=e^4,f^b=f^4,e^c=e^3f^2,f^c=ef24 conjugacy classes — view the full character table.
| maximal subgroup of | (#1043⋊C3)⋊D3, #64480⋊D3, D3×#3874⋊C2, … |
| maximal normal subgroup of | (#1043⋊C3)⋊D3, #64480⋊D3, D3×#3874⋊C2, … |
| maximal quotient of | #14268158, #14268159, #14268160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 96);