Finite Group Databasebeta

C22×#11718077 #15831198

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11718077

Splittings

FittingC22×C13×C4⋊C8 ⋊ C2
SylowC13 ⋊ C22×#331

Subgroups

subgroupG/H
centerC24#6103
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC22×C13×C4⋊C8C2
socleC24×C13C22⋊C4
prime radicalC22×#88128C2
cosocleC42×C13C24
hypercenterC22×C4⋊C8D13
hypocenterC13C22×#331
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 137847);