Finite Group Databasebeta

C2×#13112720 #15753003

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13112720

Splittings

SylowC13 ⋊ C2×#1296

Subgroups

subgroupG/H
centerC24#6103
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC22×C13×C4⋊C8C2
socle, prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenterC22×C4⋊C8D13
hypocenterC13C2×#1296
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 59652);