Finite Group Databasebeta

C2×#13131612 #16808389

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13131612

Splittings

FittingC22×C13×D8 ⋊ C4
SylowC13 ⋊ C2×#2957

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC22×C13×D8C4
socleC22×C13C2×C4×D4
prime radicalC22×#88166C2
cosocleC4×D13C25
hypercenterC22×D8#261
hypocenterC13C2×#2957
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

2642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1115038);