Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #11744634 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Hall | C52⋊C9 ⋊ C4 |
| Sylow | C52 ⋊ Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C52⋊C9 | C4 |
| Frattini | C3 | #64480 |
| Fitting, socle | C3×C52 | Dic3 |
| prime radical | C3×C5⋊D5 | D3 |
| cosocle | (C5⋊D5)⋊C9 | C2 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
Polycyclic presentation:
2^2,3^2,5^2|a^2=b,c^3=d^2,c^a=c^2d,d^a=d^2,e^a=e^3f^3,f^a=f^2,e^b=e^4,f^b=f^4,e^c=ef,f^c=e^2f^318 conjugacy classes — view the full character table.
| maximal subgroup of | #11744634⋊C2, C2×#11744634, C13×#11744634, … |
| maximal normal subgroup of | #11744634⋊C2, C2×#11744634, C13×#11744634, … |
| maximal quotient of | #14267932, C2×#11744634, C13×#11744634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 46);