Finite Group Databasebeta

#131×Dic26 #16727333

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#131×Dic26

Splittings

SylowC13 ⋊ Q8×#131

Subgroups

subgroupG/H
centerC2×C8C23×D13
commutator, socleC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC4×C13×#131C2
prime radicalC2×C13×#41C23
cosocleC2×C4×C13C25
hypercenterC4×#131D13
hypocenterC13Q8×#131
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×#131

1882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033982);