Finite Group Databasebeta

C2×#20294932 #28365501

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20294932

Splittings

SylowC109 ⋊ C2×#391

Subgroups

subgroupG/H
centerC24C22×D109
commutatorC22×C109C23×C4
FrattiniC23C23×D109
FittingC22×C42×C109C2
socle, prime radicalC24×C109C23
cosocleC23×C109C24
hypercenterC22×C42D109
hypocenterC109C2×#391
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C24 ◁ C22×C42

928 conjugacy classes of subgroups; only the 381 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 381 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6979);