Finite Group Databasebeta

C2×#99×D109 #28371483

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#99×D109

Splittings

FittingC2×#99×C109 ⋊ C2
SylowC109 ⋊ C22×#99

Subgroups

subgroupG/H
centerC22C22⋊C4×D109
commutatorC22×C109C23×C4
FrattiniC23C23×D109
FittingC2×#99×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC22×D4×D109C2
cosocleC23×C109C24
hypercenterC2×#99D109
hypocenterC109C22×#99
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

1112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 12961);