Finite Group Databasebeta

C22×#11718406 #16726406

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

Aliases

direct productC22×#11718406

Splittings

FittingC22×C13×#100 ⋊ C2
SylowC13 ⋊ C22×#413

Subgroups

subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#100C2
socleC23×C13C2×C22⋊C4
prime radicalC23×#6129C2
cosocleC2×C4×C13C25
hypercenterC22×#100D13
hypocenterC13C22×#413
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#100

5118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033055);