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#41×3−1+2⋊C4 #13153733

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×3−1+2⋊C4

Splittings

Sylow3−1+2 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×AGL(1,ℤ/9)
commutatorC2×C9C23×C3×C4
Frattini, socleC22×C3C23×C3×D3
FittingC2×#41×3−1+2C2
prime radicalC2×C32×#41D3
cosocleC22×C9C24×C3
hypercenterC2×#41AGL(1,ℤ/9)
hypocenterC9C3×C4×#41
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C2×#41

1012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72268950, C4×#41×AGL(1,ℤ/9)
maximal normal subgroup of#72268950, C4×#41×AGL(1,ℤ/9)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19796);