Finite Group Databasebeta

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C2×#14544628 #17969213

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14544628
unambiguous semidirect productD17⋊#1790

Splittings

FittingC2×C17×H(5,𝔽2) ⋊ C4
SylowC17 ⋊ C2×#1790

Subgroups

subgroupG/H
centerC22#11763750
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC2×C17×H(5,𝔽2)C4
socleC22×C17#379
prime radicalC2×H(5,𝔽2)×D17C2
cosocleC23×D17C24
hypercenterC2×H(5,𝔽2)#595
hypocenterC17C2×#1790
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C2×H(5,𝔽2)

4402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104457);