Finite Group Databasebeta

C2×#13123232 #16069015

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#13123232

Splittings

SylowC13 ⋊ C2×#2868

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C4⋊Q8C2
socle, prime radicalC24×C13C24
hypercenterC22×C4⋊Q8D13
hypocenterC13C2×#2868
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

3774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 375664);