Finite Group Databasebeta

C22×#11718511 #16730403

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11718511

Splittings

SylowC13 ⋊ C22×#477

Subgroups

subgroupG/H
centerC24C2×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×C4⋊C8C2
socle, prime radicalC24×C13C2×D4
hypercenterC22×C4⋊C8D13
hypocenterC13C22×#477
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

2358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1037052);