Finite Group Databasebeta

C2×#13117434 #16021501

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

Aliases

direct productC2×#13117434

Splittings

SylowC13 ⋊ C2×#2312

Subgroups

subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC23×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC26×C13C22
cosocleC23×C13C25
hypercenterC23×C22⋊C4D13
hypocenterC13C2×#2312
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C22⋊C4

4142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328150);