Finite Group Databasebeta

C22×#11718387 #16726348

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

Aliases

direct productC22×#11718387

Splittings

FittingC22×C13×C22⋊C8 ⋊ C2
SylowC13 ⋊ C22×#407

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×C22⋊C8C2
socleC24×C13C22×C4
prime radicalC25×D13C4
cosocleC2×C4×C13C25
hypercenterC22×C22⋊C8D13
hypocenterC13C22×#407
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

7214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1032997);