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C2×#13130680 #16797808

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13130680
unambiguous semidirect productD13⋊#1790

Splittings

FittingC2×C13×H(5,𝔽2) ⋊ C4
SylowC13 ⋊ C2×#1790

Subgroups

subgroupG/H
centerC22#11719171
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC2×C13×H(5,𝔽2)C4
socleC22×C13#379
prime radicalC2×D13×H(5,𝔽2)C2
cosocleC23×D13C24
hypercenterC2×H(5,𝔽2)#261
hypocenterC13C2×#1790
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C2×H(5,𝔽2)

4402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

166 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1104457);