Finite Group Databasebeta

C22×#16812610 #28371436

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16812610

Splittings

SylowC109 ⋊ C22×#97

Subgroups

subgroupG/H
centerC23×C4C2×D109
commutatorC2×C109C22×C42
FrattiniC2×C4C23×D109
FittingC22×C42×C109C2
socle, prime radicalC24×C109C2×C4
cosocleC2×C4×C109C24
hypercenterC22×C42D109
hypocenterC109C22×#97
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C23×C4 ◁ C22×C42

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

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, 12914);