Finite Group Databasebeta

C2×#20295506 #28376226

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20295506

Splittings

FittingC2×#117×C109 ⋊ C2
SylowC109 ⋊ C2×#520

Subgroups

subgroupG/H
centerC23C23×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
FittingC2×#117×C109C2
socleC23×C109C24
prime radicalC22×#13182029C2
cosocleC22×C109C25
hypercenterC2×#117D109
hypocenterC109C2×#520
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×#117

1640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17704);