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H(3,𝔽3)×#622 #14518584

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

Aliases

direct productH(3,𝔽3)×#622
unambiguous semidirect product(C32×#622)⋊C3

Splittings

SylowC32×H(3,𝔽3) ⋊ C8

Subgroups

subgroupG/H
center, FrattiniC2×C3C32×#157
commutatorC33C32×C8
Fitting, prime radicalC2×C32×H(3,𝔽3)C4
socleC2×C33C32×C4
cosocleC3×C3⋊Dic3C2×C32
hypercenterC2×H(3,𝔽3)#157
hypocenterC32C8×H(3,𝔽3)
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×H(3,𝔽3)

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2978);