Finite Group Databasebeta

C2×#20295703 #28376530

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20295703

Splittings

FittingC2×C22⋊Q8×C109 ⋊ C2
SylowC109 ⋊ C2×#551

Subgroups

subgroupG/H
centerC23C23×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC2×C22⋊Q8×C109C2
socleC23×C109C24
prime radicalC2×#16812669C2
hypercenterC2×C22⋊Q8D109
hypocenterC109C2×#551
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

1328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1562 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 18008);