Finite Group Databasebeta

C22×#11718524 #16730673

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11718524

Splittings

FittingC22×C13×#106 ⋊ C2
SylowC13 ⋊ C22×#481

Subgroups

subgroupG/H
centerC24D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#106C2
socleC24×C13C2×D4
prime radicalC22×#88149C2
hypercenterC22×#106D13
hypocenterC13C22×#481
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#106

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1037322);