Finite Group Databasebeta

C22⋊C4×D116 #16822315

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×D116

Splittings

FittingC4×C22⋊C4×C29 ⋊ C2
SylowC29 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC4×C22⋊C4×C29C2
socle, cosocleC23×C29C24
prime radicalC23×D116C2
hypercenterC4×C22⋊C4D29
hypocenterC29D4×C22⋊C4
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C4×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 7333);