Finite Group Databasebeta

#131×#1057 #16792589

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct product#131×#1057

Splittings

SylowC13 ⋊ C8×#131

Subgroups

subgroupG/H
centerC2×C8C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC2×C13×#131C4
socleC22×C13C22×C42
prime radicalC2×C13×#41C2×C4
cosocleC4×Dic13C24
hypercenterC2×#131#261
hypocenterC13C8×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×#131

922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1099238);