Finite Group Databasebeta

C22×#11718673 #16726765

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11718673

Splittings

SylowC13 ⋊ C22×#436

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C22×C4
prime radicalC23×D4×C13C4
cosocleC2×C4×C13C25
hypercenterC22×C4×D4D13
hypocenterC13C22×#436
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

3262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1033414);