Finite Group Databasebeta

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C22×H(5,𝔽2)×D71 #32911337

order18176
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C220

Aliases

direct productC22×H(5,𝔽2)×D71

Splittings

FittingC22×H(5,𝔽2)×C71 ⋊ C2
SylowC71 ⋊ C23×H(5,𝔽2)

Subgroups

subgroupG/H
centerC23C24×D71
commutator, cosocleC2×C71C27
FrattiniC2C26×D71
FittingC22×H(5,𝔽2)×C71C2
socleC23×C71C25
hypercenterC22×H(5,𝔽2)D71
hypocenterC71C23×H(5,𝔽2)
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×H(5,𝔽2)

65726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

2516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1083453);