Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #11744707 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C52 ⋊ C4 |
| Sylow | C52 ⋊ #157 |
| Sylow | C32 ⋊ #1043 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52 | C4 |
| prime radical, cosocle | C3⋊(C3⋊(C5⋊D5)) | C2 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
Polycyclic presentation:
2^2,3^2,5^2|a^2=b,c^a=cd,d^a=cd^2,e^a=e^2,f^a=f^2,c^b=c^2,d^b=d^2,e^b=e^4,f^b=f^460 conjugacy classes — view the full character table.
| maximal subgroup of | #14268407, #14268447, D5⋊#4380, … |
| maximal normal subgroup of | #14268407, #14268447, D5⋊#4380, … |
| maximal quotient of | #14268211, C2×#11744707, C13×#11744707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 119);