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C2×#10588045 #11765645

order1134
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC2×#10588045

Splittings

FittingC2×C7×3−1+2 ⋊ C3
HallC2×C7 ⋊ #731
SylowC7 ⋊ C2×#731

Subgroups

subgroupG/H
centerC2×C3C7⋊H(3,𝔽3)
commutator, cosocleC32×C7C2×C32
FrattiniC32C2×C3×ΓL(1,𝔽8)
FittingC2×C7×3−1+2C3
socleC2×C3×C7H(3,𝔽3)
prime radicalC2×C7⋊H(3,𝔽3)C3
hypercenterC2×3−1+2ΓL(1,𝔽8)
hypocenterC7C2×#731
LCSG ▷ C32×C7 ▷ C3×C7 ▷ C7
UCSC1 ◁ C2×C3 ◁ C2×C32 ◁ C2×3−1+2

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 378

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 75);