Finite Group Databasebeta

C2×#20295087 #28371658

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

Aliases

direct productC2×#20295087

Splittings

SylowC109 ⋊ C2×#433

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC22×C109C23×C4
FrattiniC2×C4C23×D109
FittingC2×#117×C109C2
socleC23×C109C22×C4
prime radicalC24×C109C2×C4
cosocleC2×C4×C109C24
hypercenterC2×#117D109
hypocenterC109C2×#433
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×#117

412 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 229 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) = 6976

Conjugacy classes & character table

2216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13136);