Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C5×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ Dic5 |
| Sylow | C5 ⋊ #1084 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C3⋊D15 |
| commutator, hypocenter | C5×H(3,𝔽3) | C4 |
| Fitting, prime radical, cosocle | C2×C5×H(3,𝔽3) | C2 |
| socle | C2×C3×C5 | C3⋊D3 |
| LCS | G ▷ C5×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^2,3^2,5,3|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | #11761729, D5×#1084, Dic5×#272, … |
| maximal normal subgroup of | #11761729, D5×#1084, Dic5×#272, … |
| maximal quotient of | #11761701, C2×#10587367, #13108150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 27);