Finite Group Databasebeta

C2×#13114354 #15845547

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#13114354

Splittings

SylowC13 ⋊ C2×#1694

Subgroups

subgroupG/H
centerC23#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#446C2
socle, prime radicalC23×C13#121
hypercenterC2×#446D13
hypocenterC13C2×#1694
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#446

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 152196);