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H(3,𝔽3)×C3⋊(C3⋊C8) #14517870

order1944
automorphism?
homologyAbelianization (H1) = C32×C8 · Schur multiplier (H2) = C33

Aliases

direct productH(3,𝔽3)×C3⋊(C3⋊C8)
unambiguous semidirect productC3⋊(C3⋊C8×H(3,𝔽3))

Splittings

SylowC32×H(3,𝔽3) ⋊ C8

Subgroups

subgroupG/H
center, FrattiniC3×C4C32×C3⋊D3
commutatorC33C32×C8
FittingC32×C4×H(3,𝔽3)C2
socleC2×C33C32×C4
prime radicalC2×C32×H(3,𝔽3)C4
cosocleC33×C4C2×C32
hypercenterC4×H(3,𝔽3)C3⋊D3
hypocenterC32C8×H(3,𝔽3)
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C3×C4 ◁ C4×H(3,𝔽3)

840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2264);