Finite Group Databasebeta

C2×#20295322 #28372804

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

Aliases

direct productC2×#20295322

Splittings

SylowC109 ⋊ C2×#477

Subgroups

subgroupG/H
centerC23C2×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×C4⋊C8×C109C2
socle, prime radicalC23×C109C2×D4
hypercenterC2×C4⋊C8D109
hypocenterC109C2×#477
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

416 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 173 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

2198 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 14282);