Finite Group Databasebeta

C4×#11745291 #16822014

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#11745291

Splittings

FittingC22×C42×C29 ⋊ C2
SylowC29 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D29
commutatorC22×C29C23×C4
FrattiniC23C23×D29
FittingC22×C42×C29C2
socle, cosocleC23×C29C24
prime radicalC22×C22⋊D29C22
hypercenterC22×C42D29
hypocenterC29C4×#123
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C22×C42

688 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, 7032);