Finite Group Databasebeta

C22×#11745231 #16832768

order3712
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11745231

Splittings

SylowC29 ⋊ C22×C4⋊Q8

Subgroups

subgroupG/H
centerC24C22×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC22×C42×C29C2
socle, prime radicalC24×C29C23
hypercenterC22×C42D29
hypocenterC29C22×C4⋊Q8
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C24 ◁ C22×C42

1624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

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, 17786);