Finite Group Databasebeta

C2×#13129866 #16788675

order3328
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13129866

Splittings

SylowC13 ⋊ C2×#1370

Subgroups

subgroupG/H
centerC22×C4C4⋊#261
commutatorC4×C13C22×C16
FrattiniC42C22×#261
FittingC2×C4×C8×C13C4
socle, prime radicalC23×C13C4⋊C8
cosocleC4×#1055C23
hypercenterC2×C4×C8#261
hypocenterC13C2×#1370
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1095324);