Finite Group Databasebeta

C2×#13131686 #16808626

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13131686

Splittings

SylowC13 ⋊ C2×#2972

Subgroups

subgroupG/H
centerC23C23×#261
commutatorC2×C13C24×C8
FrattiniC22C24×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C23×C4
prime radicalC23×D52C4
cosocleC2×Dic13C25
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#2972
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

2890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1115275);