Finite Group Databasebeta

C2×#20295711 #28376539

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

Aliases

direct productC2×#20295711

Splittings

FittingC22×C4⋊C4×C109 ⋊ C2
SylowC109 ⋊ C2×#552

Subgroups

subgroupG/H
centerC23C23×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC22×C4⋊C4×C109C2
socleC23×C109C24
prime radicalC22×C22⋊D109C22
hypercenterC22×C4⋊C4D109
hypocenterC109C2×#552
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×C4⋊C4

1124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 18017);