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C2×#10588065 #11765765

order1134
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C32

Aliases

direct productC2×#10588065

Splittings

FittingC2×C7×3−1+2 ⋊ C3
HallC2×C7 ⋊ #737
SylowC7 ⋊ C2×#737

Subgroups

subgroupG/H
centerC2×C3C32×ΓL(1,𝔽8)
commutator, cosocleC3×C7C2×C33
FrattiniC3C2×C32×ΓL(1,𝔽8)
FittingC2×C7×3−1+2C3
socleC2×C3×C7C33
prime radicalC2×C7⋊H(3,𝔽3)C3
hypercenterC2×3−1+2ΓL(1,𝔽8)
hypocenterC7C2×#737
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 378

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 195);