Finite Group Databasebeta

C22×#11718117 #15828705

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11718117

Splittings

SylowC13 ⋊ C22×#323

Subgroups

subgroupG/H
centerC24C22⋊Dic13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC23×C13×C22⋊C4C2
socleC24×C13C22⋊C4
prime radicalC26×C13C4
cosocleC22×C4×C13C24
hypercenterC23×C22⋊C4D13
hypocenterC13C22×#323
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×C22⋊C4

2878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 135354);