Finite Group Databasebeta

C2×#99×#261 #16796961

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#99×#261

Splittings

FittingC2×C13×#99 ⋊ C4
SylowC13 ⋊ C2×C4×#99

Subgroups

subgroupG/H
centerC22C22⋊C4×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC2×C13×#99C4
socleC22×C13C4×C22⋊C4
prime radicalC22×D4×D13C22
cosocleC23×D13C24
hypercenterC2×#99#261
hypocenterC13C2×C4×#99
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

2242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103610);