Finite Group Databasebeta

C22×#16812659 #28376200

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16812659

Splittings

FittingC22×C22⋊C4×C109 ⋊ C2
SylowC109 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC24C22×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
FittingC22×C22⋊C4×C109C2
socleC24×C109C23
prime radicalC23×C22⋊D109C2
cosocleC22×C109C25
hypercenterC22×C22⋊C4D109
hypocenterC109C22×C4×D4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C24 ◁ C22×C22⋊C4

2528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17678);