Finite Group Databasebeta

C22×#11718122 #15860361

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11718122

Splittings

SylowC13 ⋊ C22×#343

Subgroups

subgroupG/H
centerC24C22⋊Dic13
commutatorC22×C13C22×C42
FrattiniC22×C4C23×D13
FittingC23×C13×C4⋊C4C2
socleC24×C13C22⋊C4
prime radicalC25×C13C2×C4
cosocleC22×C4×C13C24
hypercenterC23×C4⋊C4D13
hypocenterC13C22×#343
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×C4⋊C4

2494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167010);