Finite Group Databasebeta

C22×#11718403 #16729637

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11718403

Splittings

FittingC22×C13×#99 ⋊ C2
SylowC13 ⋊ C22×#458

Subgroups

subgroupG/H
centerC23#88136
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#99C2
socleC23×C13#120
prime radicalC22×#88251C2
hypercenterC22×#99D13
hypocenterC13C22×#458
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

5294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1036286);