Finite Group Databasebeta

C22×#16812693 #28376288

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#16812693

Splittings

FittingC22×C42×C109 ⋊ C2
SylowC109 ⋊ C22×#126

Subgroups

subgroupG/H
centerC24C22×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC22×C42×C109C2
socleC24×C109C23
prime radicalC24×D109C22
hypercenterC22×C42D109
hypocenterC109C22×#126
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C24 ◁ C22×C42

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17766);