Finite Group Databasebeta

C2×#20294831 #28364735

order13952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20294831

Splittings

SylowC109 ⋊ C2×#358

Subgroups

subgroupG/H
centerC23D872
commutatorC8×C109C22×C4
FrattiniC2×C8C22×D109
FittingC22×C16×C109C2
socle, prime radicalC23×C109D8
cosocleC2×C8×C109C23
hypercenterC22×C16D109
hypocenterC109C2×#358
LCSG ▷ C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

232 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 101 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

3500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6213);