Finite Group Databasebeta

C2×#20295837 #28377792

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20295837

Splittings

FittingC2×H(5,𝔽2)×C109 ⋊ C2
SylowC109 ⋊ C2×#577

Subgroups

subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC4×C109C25
FrattiniC4C24×D109
FittingC2×H(5,𝔽2)×C109C2
socleC22×C109C22×D4
hypercenterC2×H(5,𝔽2)D109
hypocenterC109C2×#577
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×H(5,𝔽2)

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 19270);