Finite Group DatabasebetaFinite Group Databasebeta| order | 450 |
| isoclinism | isoclinic class of #90646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C52⋊C9 ⋊ C2 |
| Sylow | C52 ⋊ D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52⋊C9 | C2 |
| Frattini | C3 | #3874 |
| Fitting, socle | C3×C52 | D3 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 45 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,7)(2,4,6,13,5,9,12,10,11,14)(3,15)(17,19)(18,22)(20,21)(23,24);(1,2,4)(3,6,14)(5,10,8)(7,11,13)(9,15,12)(16,24,19,22,21,20,18,17,23)Polycyclic presentation:
2,3^2,5^2|b^3=c^2,b^a=b^2c,c^a=c^2,e^a=d^4e^4,d^b=de^3,e^b=d^4e^324 conjugacy classes — view the full character table.
| maximal subgroup of | #90646⋊C2, C2×#90646, C3×#90646, … |
| maximal normal subgroup of | #90646⋊C2, C2×#90646, C3×#90646, … |
| maximal quotient of | #11744607, C2×#90646, #13062464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(450, 11);