Finite Group Databasebeta

C2×#13113023 #15783378

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13113023

Splittings

SylowC13 ⋊ C2×#1418

Subgroups

subgroupG/H
centerC22#11718154
commutatorC13×C16C22×C4
FrattiniC2×C16C22×D13
Fitting, prime radicalC2×C13×#508C2
socleC22×C13#357
cosocleC2×C13×C16C23
hypercenterC2×#508D13
hypocenterC13C2×#1418
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#508

302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 90027);