Finite Group Databasebeta

C2×#20295133 #28371819

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

Aliases

direct productC2×#20295133

Splittings

SylowC109 ⋊ C2×#441

Subgroups

subgroupG/H
centerC23D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
FittingC22×Q16×C109C2
socle, prime radicalC23×C109C2×D4
cosocleC2×C4×C109C24
hypercenterC22×Q16D109
hypocenterC109C2×#441
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

480 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 237 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

1556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13297);