Finite Group Databasebeta

C2×#131×#261 #16808013

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#131×#261

Splittings

FittingC2×C13×#131 ⋊ C4
SylowC13 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C8C22×#261
commutatorC2×C13C23×C42
FrattiniC4C24×#261
FittingC2×C13×#131C4
socleC22×C13C22×C42
prime radicalC2×#41×D13C22
cosocleC4×D13C25
hypercenterC2×#131#261
hypocenterC13C2×C4×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×#131

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114662);