Finite Group Databasebeta

C2×#20294790 #28362755

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20294790

Splittings

SylowC109 ⋊ C2×#341

Subgroups

subgroupG/H
centerC22×C4C22⋊D109
commutatorC4×C109C2×C42
FrattiniC22×C4C22×D109
FittingC22×M16×C109C2
socleC23×C109C4⋊C4
prime radicalC24×C109Q8
cosocleC22×C4×C109C23
hypercenterC22×M16D109
hypocenterC109C2×#341
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 4233);