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C2×H(3,𝔽4)×D71 #32904323

order18176
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C211×C42

Aliases

direct productC2×H(3,𝔽4)×D71

Splittings

FittingC2×H(3,𝔽4)×C71 ⋊ C2
SylowC71 ⋊ C22×H(3,𝔽4)

Subgroups

subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×H(3,𝔽4)×C71C2
socleC23×C71C25
hypercenterC2×H(3,𝔽4)D71
hypocenterC71C22×H(3,𝔽4)
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×H(3,𝔽4)

10246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1076439);