Finite Group Databasebeta

C22×#11718402 #16729633

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC22×#11718402

Splittings

FittingC22×C13×#99 ⋊ C2
SylowC13 ⋊ C22×B(4,𝔽2)

Subgroups

subgroupG/H
centerC23#88136
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#99C2
socleC23×C13#120
hypercenterC22×#99D13
hypocenterC13C22×B(4,𝔽2)
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

7014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036282);