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C2×#1088⋊C32 #14519280

order1944
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×#1088⋊C32
unambiguous semidirect product(C2×#1088)⋊C32
unambiguous semidirect product(C2×C3×#1088)⋊C3

Splittings

FittingC2×H(5,𝔽3) ⋊ C4
SylowH(5,𝔽3) ⋊ C2×C4

Subgroups

subgroupG/H
center, socleC2×C3C32×#157
commutator, hypocenterH(3,𝔽3)C2×C32×C4
FrattiniC3C2×C32×#157
FittingC2×H(5,𝔽3)C4
prime radicalC2×#92392C2
cosocle#272C22×C32
hypercenterC2×H(3,𝔽3)#157
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C2×C3 ◁ C2×H(3,𝔽3)

362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3674);