Finite Group Databasebeta

C22⋊C4×#6129 #16022116

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22⋊C4×#6129

Splittings

FittingD4×C13×C22⋊C4 ⋊ C2
SylowC13 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingD4×C13×C22⋊C4C2
socle, cosocleC23×C13C25
prime radicalC23×#6129C2
hypercenterD4×C22⋊C4D13
hypocenterC13C22⋊C4×#41
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ D4×C22⋊C4

5646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328765);