Finite Group Databasebeta

C2×#13112896 #15774282

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13112896

Splittings

SylowC13 ⋊ C2×#1366

Subgroups

subgroupG/H
centerC22#11718073
commutatorC42×C13C22×C4
FrattiniC4×C8C22×D13
FittingC2×C13×#364C2
socleC22×C13#333
prime radicalC23×C13#100
cosocleC4×C8×C13C23
hypercenterC2×#364D13
hypocenterC13C2×#1366
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#364

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 80931);