Finite Group Databasebeta

C2×#13115289 #15864700

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13115289

Splittings

FittingC23×C13×C22⋊C4 ⋊ C2
SylowC13 ⋊ C2×#1898

Subgroups

subgroupG/H
centerC23C2×#6103
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC23×C13×C22⋊C4C2
socleC23×C13C2×C22⋊C4
prime radicalC22×#88207C2
cosocleC24×C13C24
hypercenterC23×C22⋊C4D13
hypocenterC13C2×#1898
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C26 ◁ C23×C22⋊C4

3746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171349);