Finite Group Databasebeta

C22×#16812638 #28376127

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16812638

Splittings

FittingC22×C16×C109 ⋊ C2
SylowC109 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C8C2×D109
commutatorC2×C109C23×C8
FrattiniC8C23×D109
FittingC22×C16×C109C2
socleC23×C109C2×C8
prime radicalC23×D109C8
cosocleC8×C109C24
hypercenterC22×C16D109
hypocenterC109C22×M32
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C8 ◁ C22×C16

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17605);