Finite Group Databasebeta

C2×#20294946 #28366242

order13952
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20294946

Splittings

SylowC109 ⋊ C2×#395

Subgroups

subgroupG/H
centerC24C22×D109
commutator, cosocleC23×C109C24
FrattiniC23C23×D109
FittingC22×C4⋊C4×C109C2
socle, prime radicalC24×C109C23
hypercenterC22×C4⋊C4D109
hypocenterC109C2×#395
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C24 ◁ C22×C4⋊C4

908 conjugacy classes of subgroups; only the 277 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Conjugacy classes & character table

2204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 7720);