Finite Group Databasebeta

C22×#11718121 #15860314

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11718121

Splittings

SylowC13 ⋊ C22×#340

Subgroups

subgroupG/H
centerC25C22⋊D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC23×C13×C4⋊C4C2
socle, prime radicalC25×C13D4
cosocleC22×C4×C13C24
hypercenterC23×C4⋊C4D13
hypocenterC13C22×#340
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 166963);