Finite Group Databasebeta

C22×#11719650 #16776811

order3328
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C220

Aliases

direct productC22×#11719650

Splittings

FittingC22×C13×H(5,𝔽2) ⋊ C2
SylowC13 ⋊ C22×#585

Subgroups

subgroupG/H
centerC23C24×D13
commutator, cosocleC2×C13C27
FrattiniC2C26×D13
FittingC22×C13×H(5,𝔽2)C2
socleC23×C13C25
hypercenterC22×H(5,𝔽2)D13
hypocenterC13C22×#585
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×H(5,𝔽2)

60366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1083460);