Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C32 |
| direct product | Dic5×H(3,𝔽3) |
| unambiguous semidirect product | (C32×Dic5)⋊C3 |
| Hall | C5×H(3,𝔽3) ⋊ C4 |
| Sylow | C5 ⋊ C4×H(3,𝔽3) |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | H(3,𝔽3)×#170, (C3⋊(C3⋊#170))⋊C3, #11761726, … |
| maximal normal subgroup of | H(3,𝔽3)×#170, (C3⋊(C3⋊#170))⋊C3, #11761726, … |
| maximal quotient of | H(3,𝔽3)×#168, C2×Dic5×H(3,𝔽3), Dic5×C32⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 14);