Finite Group Databasebeta

← Prev (#13091023) Next (#13091025) →

3−1+2×D27 #13091024

order1458
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C1

Aliases

direct product3−1+2×D27

Splittings

Fitting, SylowC27×3−1+2 ⋊ C2

Subgroups

subgroupG/H
centerC3C32×D27
commutator, cosocleC3×C27C2×C32
FrattiniC3×C9C32×D3
FittingC27×3−1+2C2
socleC32C32×D9
prime radicalC32×D27C3
hypercenter3−1+2D27
hypocenterC27C2×3−1+2
LCSG ▷ C3×C27 ▷ C27
UCSC1 ◁ C3 ◁ 3−1+2

103 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1098);