Finite Group Databasebeta

C22×#11745238 #16832748

order3712
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11745238

Splittings

FittingC22×C42×C29 ⋊ C2
SylowC29 ⋊ C22×#126

Subgroups

subgroupG/H
centerC24C22×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC22×C42×C29C2
socleC24×C29C23
prime radicalC24×D29C22
hypercenterC22×C42D29
hypocenterC29C22×#126
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C24 ◁ C22×C42

1320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 17766);