Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C5×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ Dic5 |
| Sylow | C5 ⋊ #1088 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #4379 |
| commutator, Fitting, hypocenter | C5×H(3,𝔽3) | C4 |
| socle | C3×C5 | #157 |
| prime radical, cosocle | C5×#272 | C2 |
| LCS | G ▷ C5×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
Polycyclic presentation:
2^2,3^2,5,3|a^2=b,c^a=c^2d,d^a=cdf,e^a=e^4,c^b=c^2,d^b=d^2f,d^c=df^234 conjugacy classes — view the full character table.
| maximal subgroup of | #11761921, D5×#1088, (((C3⋊D3)⋊C3)⋊C2)⋊D5, … |
| maximal normal subgroup of | #11761921, D5×#1088, (((C3⋊D3)⋊C3)⋊C2)⋊D5, … |
| maximal quotient of | #11761728, C2×#10587382, C3×#10587382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 42);