Finite Group Databasebeta

C2×#20294990 #28371468

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20294990

Splittings

SylowC109 ⋊ C2×#407

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC22×C109C23×C4
FrattiniC2×C4C23×D109
FittingC24×C4×C109C2
socleC23×C109C22×C4
prime radicalC25×C109C4
cosocleC2×C4×C109C24
hypercenterC24×C4D109
hypocenterC109C2×#407
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C24×C4

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

3512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 12946);