Finite Group Databasebeta

C2×#13117308 #16021289

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#13117308

Splittings

SylowC13 ⋊ C2×#2295

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#376C2
socle, prime radicalC24×C13C24
cosocleC23×C13C25
hypercenterC2×#376D13
hypocenterC13C2×#2295
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×#376

2750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327938);